Corruption and Gouvernance Problem

UNIVERSITY OF CALIFORNIA, IRVINE

Essays on Corruption and Governance

DISSERTATION

Submitted in partial satisfaction of the requirements for the degree of

DOCTOR OF PHILOSOPHY

in Economics

by

Amjad Toukan

Dissertation Committee:

Stergios Skaperdas, Chair Michelle Garfmkel

Priya Ranjan Donald Saari

2007

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UMI Number: 3271334

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Committee Chair

University of California, Irvine 2007

ii


DEDICATION

To

My Mother, Father, Aiman, Yassar, Nancy my beloved wife, and our newMohammad:

The true inspiration in my life

iii


TABLE OF CONTENTS

Page

LIST OF FIGURES vi

LIST OF TABLES vii

ACKNOWLEDGEMENTS viii

CURRICULUM VITAE ix

ABSTRACT OF THE DISSERTATION xi

Introduction 1

Chapter 1: Privately Held or Publicly Owned? Large Shareholders and

Corporate Control 5

1.1 Introduction 5

1.2 The model 10

1.3 Equilibrium choices where the partners compete in

an asymmetric contest for control 15

1.4 Equilibrium choices where the partners compete with

the powers of persuasion 21

1.5 Concluding remarks 27

Chapter 2: Risk of Expropriation and the Rybczynski Theorem 33

2.1 Introduction 33

2.2 The model 37

2.3 Data description 45

2.4 Empirical Results 48

2.5 Concluding remarks 56

iv


Chapter 3: Contests with a Generalized Difference Form 58

3.1 Introduction 58

3.2 Persuasion Function as an Alternative to the

Tullock Functional Form 63

3.3 The symmetric case 65

3.4 Non-cooperative equilibrium with asymmetric cost

functions and asymmetric contestable rents 69

3.5 Non-cooperative equilibrium with asymmetric

evidence production 72

3.6 Non-cooperative pure strategy equilibria with N agents 75

3.7 Persuasion with a fixed number of agents N 77

3.8 Non-cooperative equilibrium and the extent of rent

dissipation 78

3.9 Non-cooperative equilibrium - asymmetric case 80

3.10 Conclusion 86

Appendix 87

BIBLIOGRAPHY 93

v


LIST OF FIGURES

Page

Figure 1.1 The game between shareholders and managers 11

Figure 1.2 Optimal value to owners/ managers (the partners

compete in an asymmetric contest for control) 29

Figure 1.3 Optimal ownership structure to owners/ managers

(the partners compete in an asymmetric contest for control) 30

Figure 1.4 Optimal value to owners/ managers (the partners

compete with the powers of persuasion) 31

Figure 1.5 Optimal ownership structure to owners/ managers (the partners

compete with the powers of persuasion) 32

Figure 2.1 Equilibrium analysis 40

Figure 3.1 Player 1 ’s reaction curve 67

Figure 3.2 Non-cooperative pure strategy equilibrium 69

c cFigure 3.3 Non-cooperative pure strategy equilibrium - —L < 72X\ X 2

Figure 3.4 Non-cooperative pure strategy equilibrium -(1-6) <6 75

Figure 3.5 Non-cooperative pure strategy equilibrium - asymmetric

example 1 84

Figure 3.6 Non-cooperative persuasion equilibrium - asymmetric

example 2 84


LIST OF TABLES

Table 2.1 Comparison table for Japan and Venezuela

Table 2.2 Estimating Rybczynski effects for a sample of

22 OECD countries

Table 2.3 Estimating Rybczynski effects for a sample of

16 developing countries

Page

35

51

53

vii


ACKNOWLEDGEMENTS

I am indebted to Professor Stergios Skaperdas for his constant guidance,

encouragement and support. Professor Skaperdas was not only my advisor, he was

also my mentor who gave his endless intellectual and moral support that played an

invaluable role in the timely completion of this project. I am also very grateful to

Professor Donald Saari, Professor Michelle Garfinkel and Professor Priya Ranjan for

their valuable feedback and thought-provoking suggestions at different stages in the

development of this work.

I am very grateful to the Department of Economics at UCI, the Institute for

Mathematical Behavioral Sciences (IMBS) at UCI for their generous financial

support.

viii


CURRICULUM VITAE

Amjad Toukan

EDUCATION

2007 Ph.D. in Economics, University of California, Irvine

2001 MBA, University of California, Irvine

1988 M.Sc. in Electrical Engineering, California State University, Fullerton

1986 B.Sc. in Electrical Engineering, University of California, Irvine

FIELDS OF SPECIALIZATION

Applied Microeconomic Theory, Public Choice/Political Economy,

International Trade

HONORS, SCHOLARSHIPS AND FELLOWSHIPS

Regents Fellowship, Summer 2005, Department of Economics, UC-Irvine

Regents Fellowship, Summer 2004, Department of Economics, UC-Irvine

Summer Fellowship, Summer 2002 and 2003, Institute for Mathematical and

Behavioral Sciences, UC-Irvine

Invited Panelist to the Teaching Assistant Professional Development Program,

2003-2004

Dean’s Letter for Outstanding Teaching Evaluations, Fall 2002, Spring 2003,

Winter 2005

ix


Sarah Scaife Foundation Scholarship to attend Public Choice Outreach

Conference at George Mason University, Fairfax, Virginia (2004)

TEACHING EXPERIENCE

Summer 2005: Teaching Associate, Department of Economics, UC-Irvine

Summer 2004: Teaching Associate, Department of Economics, UC-Irvine

Spring 2002: Teaching Associate, School of Social Science, UC-Irvine

Fall 2000 to present: Teaching Assistant, School of Social Science, UC-Irvine

PROFESSIONAL ACTIVITIES

Conference Participation: Public Choice Society Meeting, (2004); Public

Choice

Outreach Conference (2004)

Referee: Economic Theory

Conference Organization: Assisted Prof. Donald Saari in organizing the

graduate student conference on social choice and behavioral sciences, 2004


ABSTRACT OF THE DISSERTATION

Essays on Corruption and Governance

by

Amjad Toukan

Doctor of Philosophy in Economics

University of California, Irvine, 2007

Professor Stergios Skaperdas, Chair

Nearly 2500 years ago, the old Indian treatise entitled “Arthashastra” had recognized

the impact of corruption on the conduct of the economy. Corruption is not just an

economic problem, however; it is also associated with bad governance (governance

being defined as the way in which both public and private institutions perform their

functions in a country). In my dissertation, I focus on the principal-agent model of

corruption. The agency relationship links at least two actors and is the basic unit of

analysis. The first chapter evaluates a corporation’s decision to go public, draws the

distinction between large and dispersed shareholders and examines how the

differences in their incentives to monitor the managers affect the shape of ownership

structure in public firms. In the second chapter, I find evidence contradicting the

predictions of the Rybczynski theorem using a sample of 28 manufacturing industries

in 16 developing countries over eight years. This contradiction is examined using a

modification of the Heckscher-Ohlin model to allow for international variability in

corruption and risk of expropriation. The final chapter explores the properties and

implications of a general class of “difference-form” contests that has been derived for

settings in which rent-seeking involves persuasion. Such class of contests could be

xi


employed to analyze the impact of corruption in governance such as the decision

making in the courtroom, the decision making within bureaucracies, the interactions

among interest groups among others.

xii


Introduction

Nearly 2500 years ago, the old Indian treatise entitled “Arthashastra” had recognized

the impact of corruption on the conduct of the economy. Chanakya in Arthashastra

urged the king’s administrators to control the state income and expenses in order to

avoid embezzlement of state funds. Corruption is not just an economic problem,

however; it is also associated with bad governance (governance being defined as the

way in which both public and private institutions perform their functions in a

country). Ineffective formal governance institutions lead to the creation of informal

institutions to substitute for the functions that the formal ones are unable to perform.

Corruption at high levels of government has even a more profound impact on the

degree of informality: it forms barriers to entry by creating a less competitive

business environment and adds to business risks by increasing the unpredictability of

government policies [Johnson, Kaufmann, and Shleifer (1997)].

Following Becker and Stigler [1974], Banfield [1975], Rose-Ackerman [1975,

1978], and Klitgaard [1988, 1991] my research will focus on the principal-agent

model of corruption. The agency relationship links at least two actors and is the basic

unit of analysis. Whenever there is a potential conflict of interest between the

principals and the principals' agents, the principals are induced to limit the extent to

which the agents may seek to further their own interests rather than those of the

principals. Agency costs are incurred when agents do not maximize principals’

1


Stephane

Texte surligné

objectives and when principals spend time and money to monitor agents and to

influence their actions.

The first chapter “Privately Held or Publicly Owned? Large Shareholders

and Corporate Control” examines the decision to go public in the presence of large

and dispersed shareholders. In contrast to much of the existing literature, I make the

distinction between large and dispersed shareholders, and examine the differences in

their incentives to monitor the managers. My analysis takes a game theoretic

approach, modeling the conflict between managers and shareholders as a contest.

According to Anderton (2001), one of the fundamental building blocks of a unifying

micro-theory of conflict economics is the contest success function (CSF), which

specifies how the appropriative efforts of agents lead to an appropriative outcome.

Results predicted by the use of two families of CSFs (In the first family of the CSF, a

contestant’s winning probability depends on the ratio of fighting efforts. In the second

family of the CSF, called “ difference-form” success functions, a contestant’s

probability of winning depends upon the difference of fighting efforts) are consistent

with the existing literature for example, similar to La Porta, Lopez-de-Silanes,

Shleifer and Vishny (1998), Shleifer and Wolfenzon (2002) and Burkart, Panunzi and

Shleifer (2003). In particular, I obtain a negative relationship between the

concentration of ownership shares in public companies and the legal protection of

outside shareholders. As the legal protection of outside shareholders improves,

entrepreneurs choose to decrease their share of ownership in the public firm while

increasing that of dispersed shareholders. The share of ownership sold to large

shareholders is non-monotonic in the legal protection of outside shareholders.

2


In the second chapter “Risk of Expropriation and the Rybczynski

Theorem,” I find evidence contradicting the predictions of the Rybczynski theorem

using a sample of 28 manufacturing industries in 16 developing countries over eight

years. This contradiction is examined using a modification of the Heckscher-Ohlin

model to allow for international variability in corruption and risk of expropriation.

Our model predicts that countries (with similar capital stock per worker) with higher

incidence of corruption and higher risk of expropriation have a lower ratio of capital-

intensive output to labor-intensive output. This implies that the spread of corruption

and the weak enforcement of property rights can have adverse effects on a country’s

development predicted by the ladder-of-development or product-cycle hypothesis: a

country's output mix depends on its stage of development, with countries moving

from agriculture to labor-intensive manufactures to high-tech manufacturing and

services as their aggregate labor productivity increases.

The third chapter “Contests with a Generalized Difference Form” (co

authored with Stergios Skaperdas), explores the properties and implications of a

general class of “difference-form” contests that has been derived for settings in which

rent-seeking involves persuasion. Our study characterizes equilibria and analyzes the

relationship between the extent of rent dissipation and the underlying contest

characteristics. Our results differ from those of the traditional ratio model. For

instance, in the pure-strategy equilibrium, it is possible that one or both contestants

expend zero effort. Applications of such outcomes include lobbying, election

campaigns, industrial disputes and lawsuits where one-sided submission and two-

sided peace between the parties can occur as a Cournot equilibrium. Also in contrast

3


to the traditional ratio model, we find that the extent of rent dissipation is non

monotonic in the number of contestants N while in the traditional ratio model it

strictly increasing in N.

4


Chapter 1

Privately Held or Publicly Owned? Large

Shareholders and Corporate Control

1.1 Introduction

Economists since Adam Smith have warned that a separation between ownership and

management opens the possibility of insider abuse (Enron and WorldCom scandals

are recent examples of insider abuse). The separation between ownership and

management is the principal-agent problem that occurs between shareholders and

managers and the agency costs incurred as a result of it. In our analysis we will

examine the decision to go public in the presence of both large and dispersed

shareholders and we will focus on the agency costs that are incurred due to (1) the

monitoring costs incurred by large shareholder’s in trying to keep managers’

objectives aligned with their own to maximize the value of the firm and (2) managers’

furthering their own interest rather than maximizing the value of the firm.

According to La Porta, et. al. (2000), monitoring by shareholders includes

more than just measuring or observing the behavior of the managers. It includes

efforts by shareholders to ‘control’ the behavior of the managers through budget

restrictions, compensation policies, operating rules, and other methods. The way

5


managers further their own interest (specifically expropriate shareholders) can take a

variety of forms as well. In some instances, the managers simply steal the profits. In

other instances, managers sell the output, the assets, or the additional securities in the

firm they control to another firm they own at below market-prices. Such transfer

pricing, asset stripping, and investor dilution, though often legal, have largely the

same effect as theft. In still other instances, expropriation takes the form of diversion

of corporate opportunities from the firm, installing possibly unqualified family

members in managerial positions, or overpaying executives.

Our paper joins the literature on corporate governance in the area of investor

protection. Castillo and Skaperdas (2005) examine how the legal protection of

outside shareholders and the appropriative costs that they induce influence the

incentives for private firms to go public. They model the conflict between the

owners/managers and outside shareholders as a contest to secure part of the value of

the public firm. Their findings indicate that owners are more likely to go public when

outside shareholders are better protected. In the case of going public, Castillo and

Skaperdas (2005) obtain a non-monotone relationship between the legal protection of

outside shareholders and the size of the ownership share retained by the

owners/managers. Building on their work, our paper considers not only the decision

to go public, but also the initial firm’s optimizing ownership structure in terms of the

composition of concentrated (or large) and dispersed (or small) shareholders.

We present a model of entrepreneurs who consider the possibility of taking

their company public. Absent an outright buyer, the entrepreneurs choose among two

options: they can sell a share of the company in the stock market and create a publicly

6


held firm run by the original founders or they can keep the company private. In going

public, the entrepreneurs choose the future ownership structure in a manner that

maximizes their expected payoff. In contrast to much of the existing literature, we

make the distinction between large and small shareholders, and examine the

differences in their incentives to monitor the managers. Dispersed shareholders,

having a high opportunity cost of monitoring the managers, free ride on the efforts of

large shareholders.1 Supposing that the initial owners factor in the differential

monitoring effects of large and dispersed shareholders represents a point of departure

of the analysis. This point of departure provides some insight into the large cross-

sectional differences across countries in the ownership concentration in publicly

traded firms and the possible origins of these differences. According to La Porta et.

al. (1998), the patterns of ownership vary across countries with the highest

concentration of ownership found in the French-civil-law countries and the lowest

found in a sample of East Asian countries where company law has been significantly

influenced by the United States.

1 Shleifer and Vishny (1986) show that in a corporation with many small owners, it may not pay any

one of them to monitor the performance o f the management. They build on Grossman and Hart (1980)

argument that opposite to what is often suggested, the free rider problem cannot be avoided by the use

o f the takeover bid mechanism. Outsiders without a share in a diffusely held firm would never take

over a diffusely held firm in order to improve it. The reason is that outsiders’ improvement plan would

be understood by atomistic incumbent shareholders and they will demand the value o f the

improvement in return for their shares or else they stay on. If the outsider can gain only on the shares

they already own (which are few if any) but have to pay all the monitoring and takeover costs, the deal

may not be worth their while. For the same reason, small shareholders do not have a big enough stake

in the firm to absorb the costs o f watching the management.

7


So who are the large shareholders and what characterizes their ownership

share in public firms? According to Shleifer and Vishny (1986), large shareholdings

are extremely widespread and very substantial where present. In a sample of 456 of

the Fortune 500 companies, the authors find that 354 have at least one shareholder

owning 5 percent or more of the firm. In only 15 cases does the largest shareholder

own less than 3 percent of the firm. The average holding of the largest shareholder

among the 456 firms is 15.4 percent. In their sample, large shareholders are families

represented on boards of directors (149 cases), pension and profit-sharing plans (90

cases), financial firms such as banks, insurance companies, or investment funds (117

cases) and the final category consists of firms and family holding companies with

large stakes that do not have board seats (100 cases).

Jensen and Meckling (1976), show that, in contrast to small shareholders,

large shareholders receive a discount on the price of their shares equal in value to the

cost of the efforts they exert in monitoring the managers. Specifically, they argue that

prospective large shareholders recognize that the owners/managers’ interests will

diverge somewhat from theirs; hence the highest price that they are willing to pay for

shares will reflect the monitoring costs and the effect of the divergence between the

manager’s interest and theirs.

Similar to Burkart and Panunzi (2004), we assume that large shareholders and

managers are distinct parties. Being a Board Member or even its Chairman is quite

different from being the CEO of the firm, and their interests are likely to differ. We

depart from others in assuming that there is no collusion between large shareholders

and managers in expropriating dispersed shareholders. Rather we assume that the

8


interests of the large and the dispersed shareholders are perfectly congruent. That is,

shareholders, whether large or small want the managers to maximize the firms’ value.

Our analysis takes a game theoretic approach, modeling the conflict between

managers and shareholders as a contest. According to Anderton (2001), one of the

fundamental building blocks of a unifying micro-theory of conflict economics is the

contest success function (CSF), which specifies how the appropriative efforts of

agents lead to an appropriative outcome. To date, two families of CSFs have been

developed. In one family, the conflict outcome depends on the ratio of fighting

efforts; in the other family it depends upon the difference of fighting efforts

(Hirshleifer 1995). Our main analysis incorporates the first family of the CSF where

the ratio of the efforts expended by the owners/managers and large shareholders

determines how much is appropriated by each (Clark and Riis, 1997). As a

robustness check we compare the results obtained in our main analysis with the

results obtained by the use of the other family of the CSF in which the difference of

the efforts expended by the owners/managers and large shareholders determines how

much is appropriated by each (Skaperdas and Vaidya, 2005).

Results predicted by the use of both types of CSFs are consistent with the

existing literature for example, La Porta, Lopez-de-Silanes, Shleifer and Vishny

(1997), Shleifer and Wolfenzon (2002) and Pagano and Roell (1998) show that the

better the legal protection of outside shareholders the more valuable the public firm

and the more likely that the owners of a private firm will take their company public.

Consistent with the results of La Porta, Lopez-de-Silanes, Shleifer and Vishny

(1998), Shleifer and Wolfenzon (2002) and Burkart, Panunzi and Shleifer (2003), we

9


also obtain a negative relationship between the concentration of ownership shares in

public companies and the legal protection of outside shareholders. As the legal

protection of outside shareholders improves, entrepreneurs choose to decrease their

share of ownership in the public firm while increasing that of dispersed shareholders.

The share of ownership sold to large shareholders is non-monotonic in the legal

protection of outside shareholders.

The paper is organized as follows. Section 2 outlines the model. Section 3

solves the model utilizing Tullock’s ratio-form contest success function, examines the

owner’s decision to go public and analyzes the effect of a change in the efficiency of

the legal system on the shape of the firm’s ownership structure. Section 4 solves the

model utilizing Skaperdas and Vaidya’s difference-form contest success function,

examines the owner’s decision to go public and analyzes the effect of a change in the

efficiency of the legal system on the shape of the firm’s ownership structure. Section

5 concludes.

1.2 The Model

We consider a three-stage model, where in the first stage the firm is privately owned

- that is, by its original founders, the entrepreneurs. In stage 1, the owners decide

whether to take their company public. We assume that, if they go public, they will

stay on as managers of the public firm due to their special expertise in running the

firm. A decision to go public incorporates what fraction /3 of the shares to sell to

large shareholders, what fraction a to keep, what fraction 1 - a - fi to sell to

dispersed shareholders and what fraction y of the equity sales proceeds to reinvest

10


back into the public firm. Dispersed shareholders exert no effort in protecting their

investment in the public firm. Instead they free ride on the efforts of large

shareholders in monitoring the managers. The sequence of actions in this game is

depicted in figure 1.1 below.

Stage 1;Private Finn

/ \Private Finn Public Finn

iStage 2:

i r i 1 - a - f i & a

Dispersed Large Owners/Shareholders Shareholders Managers

Large shareholders andowners/managers competefor corporate control

Figure 1.1: The game between shareholders and managers

In stage three of the game, owners/managers and large shareholders compete

for corporate control. We assume that owners/managers are forward-looking,

choosing the optimal ownership structure in stage two of the game in a manner that

maximizes their expected payoff in stage three.

According to Zingales (1995), entrepreneurs must weigh the benefits and the

costs of going public before deciding to proceed with an Initial Public Offering (IPO)

On the costs side, there are the registration and underwriting costs, the underpricing

costs (Ritter (1987)), the annual disclosure costs, and the agency problems generated

by a separation between ownership and management (Jensen and Meckling (1976)).

11


On the benefit side, there are benefits of diversification, expanding the possibility of

financing beyond the initial entrepreneurs’ limited wealth, less costly access to the

capital markets, an increased liquidity of the company’s shares, and some outside

monitoring (Holmstrom and Triole (1993)).

In our analysis we assume that the gross value of the public firm is given by

Vp (yS) , which is increasing in the amount of equity sales proceeds (yS) reinvested

back into the firm: Vp (yS) > 0 . Vf represents the market value of the private firm

and is exogenously determined. The share of the gross value of the public firm

expropriated by the owners/managers is a function, q(em,els) , depending on two

kinds of effort: em representing costly efforts exerted by the owners/managers to

expropriate part of the value of the public firm, and els representing costly efforts

exerted by large shareholders to protect their investment in the firm. Assume,

q(em, els) e [0,1], which is increasing in em and decreasing in els. 1 - q(em, els),

represents the share received by shareholders (including the owners/managers who

keep a share of the firm).

Examples of the efforts exerted by large shareholders in monitoring the

managers include auditing, formal control systems, budget restrictions, and the

establishment of incentive compensation systems, which serve to align the manager’s

interests more closely with those of shareholders. Examples of the efforts exerted by

the managers in expropriating shareholders include managers paying themselves large

salaries and generous perquisites, diverting company resources for corporate empire

building and for private benefits, and stealing business opportunities from the

company.

12


The net payoff to the owners/managers depends on the share of the firm they

can expropriate q{em,els) and the share they never relinquished a as follows:

The net value to large shareholders who own a fraction, f) , of the firm is given by:

The net value to dispersed shareholders is then given as the residual value of the

public ownership of the firm ((1 - a - fi):

Recall that dispersed shareholders, by definition are free-riders, and thus exert no

effort in the competition for corporate control. Therefore eds- 0 .

Third stage choice of efforts:

Large shareholders and owners/managers choose their equilibrium efforts

simultaneously and in a manner that maximizes their total payoffs in stage three of

the game. Given values of the owners/managers share in the public firm ( a ) , large

shareholders share ( f i ) and the value of the public firm to both large and dispersed

shareholders ( S ), the owners/managers choose em to maximize their payoff Vm

shown in (1). Similarly large shareholders choose eb to maximize their payoff Vls

shown in (2). Assuming interior optima, e*n and e,s, these solutions are defined

implicitly by the respective first order conditions as functions of a , p and yS .

Substituting the equilibrium efforts e*m and e*s into equations (1) and (2) above we

K ,(em,eb;a,f i , jS) = (q(em,els) + a( 1 - q(em,eb))VP(yS) - em (1)

(2)

v ds ( e m ,eb;a,fi ,}S) = Q . - a - f i ) ( l - q(em, els ))VP (}S) (3)

13


get the equilibrium payoffs to the owners/managers V* and to shareholders Vs*. e„

and e*s depend on a , ft and yS , V* and /7<j are also functions of a , f) and y S .

Expected Payoff to Owners/Managers:

The expected payoff to the owners/managers from taking their private firm public

(Vo) equals the equilibrium payoff to owners/managers ( V*) plus the amount that

owners/managers ( l - y )S decide to keep from the equity sales proceeds.

V'0{a ,p ,S ) = V:(a,p,y5) + ( \ - r )S (4)

The amount (S) that shareholders are willing to pay for their share in the public firm

should equal the equilibrium payoff to shareholders ( Vs*) or the amount that

shareholders expect to receive from their share of ownership in the public firm, so

that:

5 = V*(a,fl ,yS) = V*ds(a,f3,yS) + v;s {a ,p ,y S ) (5)

Due to their added efforts in monitoring the management, large shareholders pay a

lower price for the same amount of shares than dispersed shareholders (Shleifer and

Vishny, 1986). In our model large shareholders receive a discount on the price of

their shares equal in value to the cost of the efforts they exert in monitoring the

managers.

Choosing the optimal ownership structure to owners/managers:

Owners/managers choose the proportion of shares to sell to large shareholders ( /J ),

the proportion to keep ( a ) , which together imply the proportion to sell to dispersed

shareholders (1 - a - f i ) , and the fraction ( y ) of the equity sales proceeds to keep that

14


maximize their expected payoff from taking their company public. Specifically, they

solve:

To proceed we consider specific functional forms for the contest success

function q(em,els) and for the gross value of the public firm Vp (yS). We will utilize

two different types of contest success functions (Clark and Riis (1997) and Skaperdas

and Vaidya (2005)) in the contest between managers and shareholders as illustrated in

sections III and IV below.

1.3 Equilibrium choices where the partners compete in an

asymmetric contest for control

In the third stage of the game, the competition between large shareholders and

owners/managers is modeled as a contest in which the participants exert costly efforts

to increase their probability of winning part of the value of the public firm [Clark and

Riis 1997]. What is unique about this specification is that it supposes that, even when

the two partners expend identical efforts, one of the two partners will enjoy a greater

share of the value of the firm.

The parameter o represents the effectiveness of the conflict technology or the

degree to which greater appropriative effort translates into conflict success. 6

represents the efficiency of the judiciary and law enforcement system in a country

Max(V:{a,f},YS) + { l - r )V;(a,p,y))a,p,y (6)

where o > 0. (7)

15


and it varies between 0 and 1. An increase in 6 towards 1 would indicate stronger

law enforcement or a more efficient legal system which would favor shareholders.

Conversely a movement of 6 toward 0, would indicate weaker law enforcement or a

less efficient legal system. Suppose, for example, that 6 <1/2, if both parties devoted

an equal amount of effort to the contest, the outcome would favor the original

owners/managers.

Large shareholders and owners/managers each choose their equilibrium

efforts simultaneously and in a manner that maximizes their respective net payoffs in

stage three of the game. Given values of the owners/managers share in the public

firm ( a ) , large shareholders share ([)) and the value of the public firm to both large

and dispersed shareholders ( S ) we solve for the owners/managers equilibrium efforts

by differentiating equation (1) above with respect to em and setting it equal to zero:

« \ - 0 ) e am' +9 el*)1

In order to solve for large shareholders’ equilibrium efforts, we differentiate

equation (3) above with respect to els and we set it equal to zero:

C T g q - g x y *((1 - 0 ) e ° : + d e i y

PVP(yS) = 1 (9)

Combining equations (8) and (9) above, we get:

e,s* = (10)1 — a

Plugging in equation (10) into equations (8) and (9) above, we can solve for

the owners’/managers’ and large shareholders equilibrium efforts as given by

equations (11) and (12) below:

16


^ ( l - S X l - a X J L ) "_1 - a

Pem* = ------------------- ^ — VP{yS), (11)[(i - e ) + e ( 7^ y f

1 - a

1~ a —Vp(yS), (12)[(i - e ) + e ( - ^ - y f

1 - a

Substituting (11) and (12) into (1) and (2) above we get the equilibrium

payoffs to the owners/managers and to shareholders respectively:

[a - 9)+ae m i -0)+e(.-~-yy - m - «x^-rV'm{a,p,yS) =-------- ------------------------------- --------------------- — Vp(yS) •••(13)

[ ( \ - 0 ) + d ( J ^ y f1 - a

(1 - a ) d m - 0 ) + 0 < J - y ] - <70(\ - <9)(1 - a ) ( - ? - y +l V*i.a,p,yS) = ------------------------- ^ ^ ----- Vp(y>)...(l4)

[(i - 0) + 0( - ^ - y f1 - a


We now turn to the owners/managers choice of ownership structure. This choice

factors in the effects the choices will have on els and e*m and thus on V* and V*.

Owners/managers solve:

Max (V* (a,p,yS) + ( l - r )V *(a ,p ,y ) ) (15)a,P,r

Due to the complexity in solving the maximization problem above, we will

illustrate by an example as shown below:

Example:

17


We assume that that the value of the public firm is determined through a Cobb-

Douglas-like form:

Vp(yS) = K ( y S y , whereK > 0 and ¥ is between 0 and 1 (16)

We interpret 'F , as a measure of the productivity of a public firm, which

would increase with improvements in the efficiency of the judiciary and law

enforcement system. According to Hall and Jones (1997), differences in levels of

economic success across countries are driven primarily by the institutions and

government policies (or infrastructure) that frame the economic environment in which

people produce and transact. Societies with secure physical and intellectual property

rights that encourage production are successful. Societies in which the economic

environment encourages the diversion of output instead of its production produce

much less output per worker. Diversion encompasses a wide range of activities,

including theft, corruption, litigation, and expropriation. In our analysis we will

allow for increases in VF that are commensurate with the improvements in the

efficiency of the judiciary and law enforcement system.

Plugging in (16) into (14) above, we get:

1 (1 - a)6p[{\ - 6 ) + ] - cx<9(l - <9)(1 ' ,S = r^(a,fi,yS) = K l-'i‘r 1 [ --------------------------^ ------- — -------------------- ]'-'p (17)

[(i -9)+e(T^ r f1 - a

To determine the optimal share to sell to large shareholders (5 , the optimal

share to keep a* and the optimal share to sell to dispersed shareholders (1 - a - [1) ,

we plug in (16) and (17) into the maximization problem (15) above. Due to the

difficulty in obtaining a closed form solution, we have provided a numerical solution

18


to the maximization problem as shown in figures 1.2 and 1.3 attached. Numerical

solution results show the optimal ownership structure that maximizes the expected

payoff to owners/managers for the different values of 6 (efficiency of the judiciary

and law enforcement system) and are discussed in the sections below.

Analysis of figure 1.2 attached:

Numerical solution results show that owners/managers get a higher return from

investing an additional dollar in the public firm than they would from retaining it

(except for investing in the public firm, we assume that the owners/managers earn

zero return on their money), so they reinvest the full amount of the equity sale

proceeds back into the public firm (y* =1).

In our model, we have assumed that the legal protection of outside

shareholders complements the efforts exerted by large shareholders in monitoring the

managers, so as the efficiency of the judiciary and law enforcement system improves

( Q t ), equity valuation by outside shareholders increase and the value of public firms

increase. Results obtained from our numerical solution are consistent with the

existing literature as we show that as the efficiency of the judiciary and law

enforcement system improves (0 T ), the optimal value to the owners/managers from

taking their firm public increases and the likelihood that entrepreneurs will take their

privately held firms public increases. An example with Vf 2 as the market value of

the private firm and Vq being the optimal value to the owners/managers from taking

their firm public is shown in figure 1.2 attached.


2 The value o f the private firm is exogenously determined in our model.

19


In deciding to take their company public, three sources of value contribute to the

owners/managers payoff: expropriating part of the value of the public firm; retaining

part of the proceeds received from selling equity; and the value received from being

shareholders.

In a forward looking game, the owners/managers will decide on the optimal

ownership structure in stage two of the game in a manner that maximizes their

expected payoff from taking their firm public in stage three. The owners/managers

weigh the costs and benefits of expropriation of outside investors that comes with

control. Such private benefits of control, as described by Jensen and Meckling

(1976), do come at the expense of profits accruing to the outside investors (including

the owners/managers who keep a share of the firm). In legal regimes with weak

investor protection (low values of 6 ), the owners/managers can steal a firm’s profits

perfectly efficiently and no rational outsider would finance such a firm. In such legal

regimes, the cost of raising capital to entrepreneurs is high and the family firm

emerges as the value maximizing outcome where the original owners retain both

ownership and control.

As investor protection improves or the expropriation technology becomes less

efficient, the owners/managers expropriate less, and their private benefits of control

diminish. In such situations entrepreneurs obtain outside finance on better terms. In

addition to the legal protection of outside shareholders, the presence of large

shareholders restricts managers’ excessive spending and is in the best interest of

dispersed shareholders. Pagano and Roell (1998) show that the optimal ownership

structure chosen by the entrepreneur generally involves some measure of dispersion

20


(more than one external investor). It may also involve a certain degree of monitoring

by a large external shareholder, because in order to obtain equity capital more

cheaply, the initial owner needs to restrain his own future tendency to stray. So in

legal regimes with intermediate investor protection (intermediate values of 6 ), the

optimal ownership structure chosen by entrepreneurs involves keeping the majority of

firm ownership while selling the rest of the company shares to large shareholders.

The family controlled firm emerges as the equilibrium outcome.

When legal protection of outside investors is very good (high values of 6),

there is no need for monitoring in equilibrium, and the widely held professionally

managed firm emerges as the equilibrium outcome.

Our results are consistent with La Porta, Lopez-de-Silanes, Shleifer and

Vishny (1998), Shleifer and Wolfenzon (2002) and Burkart, Panunzi and Shleifer

(2003) as we show that the concentration of ownership of shares in public companies

is negatively related to the legal protection of outside shareholders. In contrast with

Castillo and Skaperdas (2005), we obtain a negative and monotone relationship

between the legal protection of outside shareholders and the size of the ownership

share retained by the owners/managers.

1.4 Equilibrium choices where the partners compete with

the powers of persuasion

In stage three of the game, the competition between large shareholders and

owners/managers involves owners/managers and large shareholders devoting costly

21


resources to influence the opinion of a third party: Board of Directors, Securities and

Exchange Commission or the courts in their favor [Skaperdas and Vaidya 2005].

Briefly, the functional form is derived using the following process: Managers and

large shareholders expend resources em and e]s on gathering information and

evidence. The evidence and information produced are presented to the Board of

Directors, Securities and Exchange Commission or the courts. Based on the evidence

and information presented, the Board of Directors, Securities and Exchange

Commission or the courts make an inference about the truth. They update their prior

beliefs in light of the evidence and information presented and the posterior beliefs

thus produced determine the probability of their judgment being in favor or against

the claimant.

In addition to the effect that resources have in collecting information and

uncovering evidence, the efficiency of the judiciary and law enforcement system

should have an effect on the ease or difficulty with which each side can collect

information or uncover evidence in favor of its cause. In our analysis, the higher the

efficiency of the judiciary and law enforcement system the easier it is for

shareholders to collect information or uncover evidence in their favor and the harder

it is for managers to collect information or uncover evidence in theirs.

As before, the share of the gross value of the public firm received by the

owners/managers is a function of the two kinds of effort:

q(em,es)=0.5-<l>[del , O c r r c l (18)

with em representing costly efforts exerted by the owners/managers to influence the

opinion of the Board of Directors, Securities and Exchange Commission or the courts

22


in their favor, and els denotes costly efforts exerted by large shareholders to influence

the opinion of the Board of Directors, Securities and Exchange Commission or the

courts in theirs. 1 - q(em, els) represents the share of the gross value of the public

firm received by shareholders (including the owners/managers who keep a share of

the firm).

As before the parameter 6 reflects the efficiency of the judiciary and law

enforcement system in a country and it varies between 0 and 1. An increase in 6

towards 1 would indicate stronger law enforcement or a more efficient legal system.

Conversely a movement of 6 toward 0, would indicate weaker law enforcement or a

less efficient legal system. The function ea is positive, increasing and strictly

concave. The parameter (j) is taken as exogenous in our model and it varies between

0 and 0.5. In a more fully articulated model, it would be an increasing function of the

likelihood of conviction of the managers of the firm given that there is legal evidence

against them.

Solving for Equilibrium:

Large shareholders and owners/managers choose their equilibrium efforts

simultaneously and in a manner that maximizes their total payoffs in stage three of

the game. Given values of the owners/managers share in the public firm ( a ), large

shareholders share ( f t ) and the value of the public firm to both large and dispersed

shareholders ( S ) we solve for the owners/managers equilibrium efforts by

differentiating equation (1) above with respect to em and setting it equal to zero. The

owners’/managers’ equilibrium efforts are given by equation (19) below:

23


em = ( ( ! - « ) ( ! - # ) ?* O '^ ) (|“ff)5 O 9)

In order to solve for large shareholders’ equilibrium efforts, we differentiate

equation (3) above with respect to e,s and we set it equal to zero. Large shareholders’

equilibrium efforts are given by equation (20) below:

e;=(pe<|>aVp)< \ (20)

Substituting equations (19) and (20) into equations (1) and (2) above we get

the equilibrium payoffs to the owners/managers and to shareholders respectively:

V'm =Vp +0.5(a - l )Vp + ( a - 1 ) ^ 9 ) ^ (J3 V

- ((1 - a )(l - (21)

r;=O.5(l-a)F,+(l-aX00)W iP o r ) ^ V ^ c t ) < t > ( \ - V

- ( p 0 t < r ) & V & (22)


Owners/managers choose the proportion of shares to sell to large shareholders ( f t ),

the proportion to keep ( a ) , the proportion to sell to dispersed shareholders

(1 - a - (5 ) and the fraction ( y ) of the equity sales proceeds to keep in a manner that

maximizes their expected payoff from taking their company public.

Max(V;t(a,j3,yS) + (\-y)V:(a , j3 ,y)) (23)a,p,y

Due to the complexity in solving the maximization problem above, we will

illustrate by an example as shown below:

Example:

24


We assume that that the value of the public firm is determined through a Cobb-

Douglas-like form:

Vp(yS) = K ( y S f 5 whereK > 0 (24)

Substituting (24) into (22) above and in the special case of o - 0.5 , we get:

S = v;{a,p,yS) =----------------- ----------- W ~ a y K ' y ------ ...(25)[ 4 - 2 ( l - a ) p e 2f - K y + 2 ( l - a ) 2f - ( l - d ) - K 2r + J32<l>2e 2K 2r f

To determine the optimal share to sell to large shareholders , the optimal

share to owners/managers a* and the optimal share to sell to dispersed shareholders

(1 - a -/?)* , we plug in (24) and (25) into the maximization problem (23) above.

Due to the difficulty in obtaining a closed form solution, we have provided a

numerical solution to the maximization problem as shown in figures 1.4 and 1.5

attached. Numerical solution results show the optimal ownership structure that

maximizes the expected payoff to owners/managers for the different values of 6

(efficiency of the judiciary and law enforcement system) and are discussed in the

sections below.

The choice of the constant K depends in part on the value of ^ and both

values of ^ and K should be chosen in a manner that would be consistent with what

is observed in the real world. For our analysis we have chosen K to equal 20 and (f

to equal 0.25. Future work is required to get an empirical estimation for both K and

</>.


In our model, we have assumed that the legal protection of outside shareholders

complements the efforts exerted by large shareholders in monitoring the managers, so

25


as the efficiency of the judiciary and law enforcement system improves (9 T ), equity

valuation by outside shareholders increase and the value of public firms increase.

Results obtained from our numerical solution are consistent with the existing

literature as we show that as the efficiency of the judiciary and law enforcement

system improves ( 0 T ), the optimal value to the owners/managers from taking their

firm public increases and the likelihood that entrepreneurs will take their privately

held firms public increases. An example with V( 3 as the market value of the private

firm and Vq being the optimal value to the owners/managers from taking their firm

public is shown in figure 1.4 attached.


Numerical solution results show that owners/managers get a higher return from

investing an additional dollar in the public firm than they would from retaining it

(except for investing in the public firm, we assume that the owners/managers earn

zero return on their money), so they reinvest the full amount of the equity sale

proceeds back into the public firm ( y* =1).

Upon deciding to take their privately held company public, the

owners/managers have to find the particular combination of concentrated and

dispersed ownership that maximizes their wealth. Three sources of value contribute

to the owners/managers payoff: expropriating part of the value of the public firm;

retaining part of the proceeds received from selling equity; and the value received

from being shareholders.

3 The value o f the private firm is exogenously determined in our model.

26


In legal regimes with weakest shareholder protection, relatively low values of

6 , the value of the private firm exceeds its value being public (Fig. 1.4) and the

original owners decide against taking their privately held firm public. Ownership

stays with the original founders and the family owned corporation emerges as the

equilibrium outcome.

In legal regimes with intermediate shareholder protection, values of 6

midway between 0 and 1, the value of the public firm exceeds its value being private

(Fig. 1.4) and the original owners decide to take their privately held firm public.

Majority ownership stays with the original founders and the family controlled

corporation emerges as the equilibrium outcome (a* > 0.5).

In legal regimes that successfully limit the expropriation of shareholders, 6

approaching 1, the value of the public firm exceeds its value being private (Fig. 1.4)

and the original owners decide to take their privately held firm public. The widely

held corporation emerges as the equilibrium outcome.

1.5 Concluding Remarks

Our results are consistent to a large extent with the existing literature on Corporate

Governance as Burkart, Panunzi and Shleifer (2003) and Shleifer and Wolfenzon

(2002) show that firms are more valuable, shareholder expropriation is lower and

ownership concentration is lower, with better protection of shareholders. Our results

are also consistent with Burkart, Panunzi and Shleifer (2003) as they show that in

legal regimes that successfully limit the expropriation of minority shareholders, the

widely held professionally managed corporation emerges as the equilibrium outcome.

27


In legal regimes with intermediate protection, management is delegated to a

professional, but the family stays on as large shareholders to monitor the manager. In

legal regimes with the weakest protection, the founder designates his heir to manage

and ownership remains inside the family. In Western Europe for example, many

publicly traded firms are family controlled through a majority ownership while in

emerging markets such as the Middle East, both ownership and control tend to stay

with the family. In the United States, separation of ownership and control occurs at

an early stage where the original founder and his family retain only marginal

ownership.

Even though our findings are consistent to a large extent with the existing

empirical literature, measuring the correct level of legal protection of outside

shareholders ( 6 ) for different countries would be vital in interpreting empirical

results. Conflicts between shareholders and managers are not the only situations

where agency costs are incurred. We can think of the company’s overall value as a

pie that is divided among a number of claimants. These include management,

shareholders, company workforce, banks, creditors and the government. Work is

currently underway to analyze the situation where the owners raise cash from both

equity and debt financing to fund the firm’s investment decisions.

28


Optimal Value to Owners/Managers

0.6

0.4P u b l i c F i r m s

0.2

0.1 0.2 0.8 0.9 10.3 0.4 0.5 0.6 0.7

Theta

Figure 1.2: The partners compete in an asymmetric contest for control

(Vo*) Optimal Value toOwners/Managers

(Vf) Value of PrivateFirm

29


Optimal Ownership Structure to Owners/Managers1 -

0.9 |I

I0.7 4

0.6 -

0.5

0.4 -f—

0.3

0.2 4—

[

0.1

o L0.1

p*

0.2 0.3

1

0.4 0.7 0.8 0.9 10.5 0.6

Theta

Figure 1.3 : The partners compete in an asymmetric contest for control

Owners/Managers(Alpha*)

Large Shareholders (Beta*)

Dispersed Shareholders (1- Alpha*-Beta*)

30


Optimal Value to Owners/Managers

1.2 -

1 -

0.8

0.4 ■

0.2 -

/P u b l i c F i r m s

0 V 0 V <5 o - O ' O ' O ' O ' O ' O ' O ' O ' O ' O ' O ' O ' O ' O ' O ' O ' O ' O ' O ' O ' O '

Theta

Figure 1.4: The partners compete with the powers of persuasion

(Vo*) Optimal Value to Owners/Managers

(Vf) Value of Private Firm

31


Optimal Ownership Structure to Owners/Managers

Owners/Managers

■— Large Shareholders

Dispersed Shareholders

0.2

1 - a * -|3

- 0 .2 J

Theta

Figure 1.5: The partners compete with the powers of persuasion

32


Chapter 2

Risk of Expropriation and the Rybczynski Theorem

2.1 Introduction

Based on the Heckscher-Ohlin (HO) Model of international trade (see for example

Bhagwati, Srinivasan and Panagariya 1998), we can derive growth paths for

production and trade in terms of a country’s capital-labor ratio. As a country grows, it

will accumulate more capital relative to the world leading to an increase in the output

of its capital-intensive goods relative to the output of its labor-intensive goods. This

is the ladder-of-development or product-cycle hypothesis: a country's output mix

depends on its stage of development, with countries moving from agriculture to labor-

intensive manufactures to high-tech manufacturing and services as their aggregate

labor productivity increases [James Harrigan and Egon Zakrajsek, 2000]. Rybczynski

theorem formally states that “If a factor endowment in a country rises (falls), and if

prices of the outputs remain the same, then the output of the good that uses that factor

intensively will rise (fall) while the output of the other good will fall (rise).”

Harrigan (1995) and Bernstein and Weinstein (1998) used the Heckscher-

Ohlin (HO) general equilibrium model with factor price equalization to provide

empirical confirmation of Rybczynski theorem. Harrigan (1995) use data on

33


manufacturing output and factor endowments for 20 OECD countries from 1970 to

1985 and show that under well-known conditions, there will be a linear Rybczynski

relationship between sectoral outputs and factor endowments across countries.

Bernstein and Weinstein (1998) use data on production patterns and factor

endowments at the regional level for both OECD countries and Japan to verify the

Rybczynski theorem. In a recent paper, Xu [2002] focuses on developing countries,

finding capital abundance to be statistically significant in determining production

patterns in 18 of 28 examined industries. In his panel data regressions controlling for

time and country fixed effects as well as industry skill level (proxied by industry

average wage rate relative to the US), the value-added shares of 11 of the 12

relatively labor-intensive industries increase with country capital abundance, with

five of them statistically significant, and the value-added shares of 10 of the 16

relatively capital intensive industries decrease with country capital abundance, with

four of the 10 statistically significant. This finding contradicts the predictions of

Rybczynski theorem and presents the author with a puzzle.

The starting point of departure of this paper is to ask how corruption and risk

of expropriation affect the Rybczynski predictions. A preliminary analysis,

comparing data (1980-1983) for two countries with similar capital stock per worker

(K/L), reveals that the ratio of the output of capital intensive goods to the output of

labor intensive goods is higher for countries that have less corruption and higher

bureaucratic efficiency [The relevant data on corruption and the bureaucratic

efficiency index were taken from Mauro’s 1995]. Both indices, (recorded by country

representatives in each country) are subjective. The bureaucratic efficiency index is

34


the average of the judiciary system, red tape and corruption indices. The preliminary

analysis comparing data for Japan and Venezuela is shown in table 2.1 below:

Country Year K/L C/L BEI Country Year K/L C/L BEI

JPN 1981 23,345 1.72 9.08 VEN 1981 21,635 0.45 5.42

JPN 1982 24,614 1.70 9.08 VEN 1982 21,603 0.52 5.42

JPN 1983 25,785 1.70 9.08 VEN 1983 21,606 0.48 5.42K /L = capital stock per workerC/L = (value added o f capital intensive goods) / (value added o f labor intensive goods)BEI = Bureaucratic efficiency index

Table 2.1: Comparison table for Japan and Venezuela

In this paper, we use the Heckscher-Ohlin (HO) general equilibrium model to

test empirically the hypothesis that Rybczynski predictions are less likely to hold in

countries with higher risk of expropriation and higher incidence of corruption. Risk

of expropriation and incidence of corruption by corrupt government officials are

higher in the case of capital-intensive projects due to the larger size of the prize

(larger size of the pie). So in countries where the risk of expropriation and the

incidence of corruption are high, investors prefer to invest in labor-intensive projects

instead of capital-intensive projects.

Many economists argue that it is easier for a corrupt government official to

expropriate large non-standard capital-intensive projects as opposed to smaller,

standardized labor-intensive projects. Kaufmann [1998] suggests that bribing and

rent-seeking exact a significant economic cost. Corrupt bureaucrats tend to favor

non-standard, complex, and expensive capital-intensive projects that make it easier to

skim significant sums. Coolidge and Rose-Ackerman [1997], argue that kleptocrats

35


will differentially support projects that generate large corrupt payoffs. And if

revelations of corruption would destabilize the regime, the kleptocrat will favor

projects where payoffs can be easily hidden. Examples of such projects are

specialized capital-intensive projects with one of kind designs such that no one would

be able to locate a reliable cost benchmark. Coolidge and Rose-Ackerman [1997]

also point out that lacking credible commitment mechanisms, such as independent

law enforcement institutions, the corrupt autocrat may have difficulty convincing

investors to make capital investments since they may fear expropriation or

confiscatory tax and regulatory systems. The only investors willing to commit funds

may be those with a short term, get rich-quick attitude.

In conducting panel data regressions (16 developing countries over a period of

eight years 1984-1991), controlling for time and country fixed effects as well as

incidence of corruption and risk of expropriation, I find a negative and not

statistically significant relationship between capital stock per worker and the ratio of

the value-added share of the relatively capital-intensive industries to the value-added

share of the relatively labor-intensive industries. In the case of developing countries,

lack of statistical significance between capital stock per worker and the ratio of value

added share of capital intensive goods to the value added share of labor intensive

goods contradicts the predictions of the Rybczynski Theorem. A positive and

statistically significant relationship obtains between the Corruption and Expropriation

Index (the higher the Corruption and Expropriation Index the higher the incidence of

corruption and risk of expropriation) and the ratio of the value-added share of the

relatively capital-intensive industries to the value-added share of the relatively labor-

36


intensive industries. This supports the notion that the risk of expropriation and the

incidence of corruption are important factors in determining of the shape investment

structure in a country. In countries where the risk of expropriation and the incidence

of corruption are high, investors prefer to invest in labor-intensive projects instead of

capital-intensive projects.

In conducting panel data regressions (22 developed OECD countries over a

period of eight years 1984-1991), controlling for time and country fixed effects as

well as incidence of corruption and risk of expropriation, I find a positive and

statistically significant relationship between both independent variables (capital stock

per worker and the Corruption and Expropriation Index) and the ratio of the value-

added share of the relatively capital-intensive industries to the value-added share of

the relatively labor-intensive industries.

In the next section I will suggest a modification to the Heckscher-Ohlin model

where I will allow for international variability in corruption and risk of expropriation.

The modification to the Heckscher-Ohlin model is intended to explain cross country

differences in the ratio of capital-intensive output to labor intensive output and is not

intended to explain the contradiction in the predictions of Rybczynski theorem.

Results predicted by the model show that a negative relationship exists between the

risk of expropriation by corrupt government officials and the ratio of capital-intensive

output to labor-intensive output.

2.2 The Model

37


We assume that we have two countries. Each country produces two final goods, X

(capital intensive) and Y (labor intensive) using two factors of production labor and

capital. We will consider two approaches to solving our model where the same result

of higher taxation of the capital intensive good relative to the labor intensive good

obtains.

In our first approach, capital-intensive output and labor-intensive output are

subject to an expropriation tax t imposed by corrupt government officials. Risk of

expropriation by corrupt government officials is higher in the case of capital-intensive

projects due to the larger size of the prize (larger size of the pie), so we assume that

capital-intensive output is taxed at a higher rate than labor intensive output. Capital-

intensive firms maximize the following profit function:

M a x ( \ - t x )Px f x (Kx ,Lx ) - r K x - w L x (1)KX ’LX

Labor-intensive firms maximize the following profit function:

Max(\ - ty )Py f y (Ky , Ly) ~ rK y ~ WLy (2)K y ,Ly

where t x > t Y (good X is effectively taxed at a higher rate than good Y)

In our second approach, we examine the specific case of a Cobb Douglas

production function, and from our argument in section I above we assume that it is

easier for corrupt government officials to expropriate the capital endowment of firms

rather than their labor endowment. Capital-intensive firms maximize the following

profit function:

Max Px [(1 - t)(Kx ) f [Lx ]*-“ - rKx - wLx

= M a x { \ - t ) aPx [Kx ]a[Lx t a ~ r K x - w L x (3)KX’LX

38


Labor-intensive firms maximize the following profit function:

MaxPY[ ( \ - t ) (K Y)Y[LYt P - rKY - w L YK y , L y

= MOX( 1 ~ t ) PPy [Ky ] P [Ly ]'~fi ~ rK y ~ WLy (4)K y , Ly

a > ft , to guarantee that good X has a higher capital intensity than good Y

(1 - 1)“ > (1 - t)/f (good X is effectively taxed at a higher rate than good Y)

From the two approaches illustrated above, we can show that taxing the output

of individual firms effectively translates into a reduction in the relative price of the

labor intensive good X to the price of the labor intensive good Y. The effective

reduction in the relative price of good X to the price of good Y, results in an increase

in the capital to labor ratio for both goods X and Y as shown in Figure (2.1) below.

In figure 2.1 below we have equilibrium initially, with the goods-price ratio

Py Wexchanging (-J—) X for Y and with the factor-price ratio (—) at ABCD. FactorPx r

K Kproportions in X and Y are indicated by points B and C respectively with —— > ——

Lx Ly

pat all factor-price ratios. An increase in the effective goods-price ratio (— ) results

Px

in the upward shift of good X isoquant. The new equilibrium factor-price ratio is at

EFGH and it is tangential to the new (—— ,y^P--)X isoquant and the Y isoquant.0 — tx ~)Px

wThe above implies that we must have a higher factor-price ratio (—) and thus higher

r

K ratios in both sectors.L

39


Facto

r K

For any finite factor-price ratio, there must be full employment of both factors

in equilibrium. Furthermore, the overall factor-endowment ratio must be a weighted

average of the factor ratios in the two sectors, X and Y. This is shown in the identity:

( f ) = ( ^ X ~ L) + ( | L) ( ^ ) (5)J-j X Y

Where,

L "I- Ly — L

K X + K Y = K

and —^ and — are weights adding up to unity.

O Factor L

Figure 2.1: Equilibrium analysis

40


The effective reduction in the relative price of good X to the price of good Y

P K( — i ), results in an increase in the capital to labor ratio for both goods ( —— T ) and

PY L x

Y

A change in the effective goods-price ratio does not alter the amount of capital

Kand labor available in the economy and hence the ratio -j— stays the same. In order

for equation (5) to hold, we must have a decrease in the weight relative to theL

weight — . In other words Lx has to decrease and LY has to increase. From above, L

we know that —- is increasing and since LY is increasing then K Y must be LY

increasing and K x must be decreasing.

So an effective reduction in the relative price of good X to the price of good Y

p( — -I), results in a decrease in K x and Lx and an increase in K y and Ly. This

Py

implies that the output of capital-intensive goods decreases and the output of labor-

intensive goods increases.

The same result can be reached using an algebraic representation as shown in

the derivation below. Capital-intensive firms solve the following optimization

problem.

Max Px f x (K x , Lx ) — rK x — wLxKx ,PX

The first-order conditions are

41


d ° f x ( K x , L x ) _ u .

X SLX

p dfx (Kx ,Lx ) X SKX

dfx ( K x , Lx )MPT...

(6)w _ dLx _ MPLX

7 ~ 8fx (Kx ,L x r MPKx

dKx

Labor-intensive firms solve the following profit maximizing problem:

MaxPY f Y(KY,Ly) ~ rKY - wLy

the first-order conditions are

p dfY( K Y, L Y) _1 y ---------------------------------- W

dLy

dfY( K y , L Y)Y 6Ky

dfY( K Y, LY)

w _ dLy _ MPLy ^r 8fy (Ky , Ly ) MPKy

SKy

In a competitive equilibrium, each output price must equal its marginal cost,

which under the assumption of constant returns to scale equals the average cost.

Therefore we have the equations of production equilibrium:

L xP* = r ~ ^ +W^ <8)

P r E jL + w h L (9)Y Y

42


where X and Y are the outputs of the capital-intensive and labor-intensive goods

P rrespectively. Now, we define the relative prices n = — and Q = — . Dividing

PY w

equation (8) by equation (9) above, we have a functional relationship between relative

output-prices and relative factor-prices:

Q K X | Lx X XK = -

ClKy Ly

Y Y

To see whether the relative goods-price ratio is increasing or decreasing in the

relative factor-price ratio, we take the logarithms of both sides and differentiate. This

yields:

Ly Lx1 dn Ky K x

71X1 (h + K-m + K)K X Ky

Therefore a higher Q T (— T) corresponds to a higher n t (— t ) if andW Py

K Konly if —— > —— which is always true since good X is more capital-intensive than

Lx Ly

good Y.

The above also implies that an effective reduction in the relative price of good

X to the price of good Y ( —X J ,) wjH result in an increase in — AnPY Q r

Wincrease in — T will result in an increase in the marginal product of labor relative to r

the marginal product of capital for both capital-intensive and labor-intensive goods as

43


can be seen from equations (6) and (7) above. An increase in the marginal product of

labor relative to the marginal product of capital for both goods X and Y implies that

K Kthe capital to labor ratio will increase for both goods ( —— t ) and ( —— T ).

Lx LY

Adopting the same argument we used under the geometric representation above, an

increase in the capital to labor ratio for both goods X and Y will result in a decrease

in the output of capital-intensive goods and an increase in the output of labor-

intensive goods.

Our model developed above is useful in explaining cross-country differences

in the ratio of capital-intensive output to labor-intensive output. Our model predicts

that countries (with similar capital stock per worker) with higher incidence of

corruption and higher risk of expropriation have a lower ratio of capital-intensive

output to labor-intensive output. This implies that the spread of corruption and the

weak enforcement of property rights can have adverse effects on a country’s

development predicted by the ladder-of-development or product-cycle hypothesis: a

country’s output mix depends on its stage of development, with countries moving

from agriculture to labor-intensive manufactures to high-tech manufacturing and

services as their aggregate labor productivity increases [James Harrigan and Egon

Zakrajsek, 2000]. In section IV below, we use panel data collected for 22 developed

and 16 developing countries to show that an increase in the incidence of corruption

and the risk of expropriation can render the Rybczynski predictions statistically not

significant. We start by providing an illustration of the Rybczynski theorem.

The Rybczynski theorem predicts that holding product prices constant, an

increase in the relative supply of capital increases the relative output of the capital-

44


intensive good so much that the output of the labor-intensive good decline. As can be

Kshown from equation (5) above, an increase in the relative supply of capital ( — T )L

will lead to an increase in the weight -L- relative to the weight —E . In other wordsL L

L x has to increase and Ly has to decrease.

K KIf prices are constant then ( ——) and ( —- ) remain unchanged and from the

Lx Ly

goods-output ratio shown in equation (10) below, an increase in Lx relative to LY

will lead to an increase in the relative output of the capital-intensive good to the

labor-intensive good.

Y , / * ( — ->!)— = ( - ^ - ) -------- - A ( 1 0 )Y T KY Ly f A r , i)

L y

Equation (10) above defines the relationship predicted by Rybczynski theorem

which formally states that “If a factor endowment in a country rises (falls), and if

prices of the outputs remain the same, then the output of the good that uses that factor

intensively will rise (fall) while the output of the other good will fall (rise).”

2.3 Data Description

45


In this section we provide a description for the panel data collected for 22 developed

1 2(OECD) and 16 developing countries used in the empirical estimation of the model.

Subsection III.l provides a description of the corruption and risk of expropriation

index and section III.2 provides a description of the remaining variables.

2.3.1. IRIS-3 File of International Country Risk Guide (ICRG) Data - The data files

provided by the IRIS-3 file contain annual values for indicators of the quality of

governance, 1982-1997, constructed by Stephen Knack and the IRIS Center,

University of Maryland, from monthly ICRG data provided by The PRS Group.

Currently, IRIS-3 provides annual ratings for the following indicators: Corruption in

government, rule of law (law and order tradition), bureaucratic quality, ethnic

tensions, repudiation of contracts by government, and risk of expropriation. To

measure the incidence of corruption and risk of expropriation in a country, I took the

simple average of the risk of expropriation and corruption indices. The IRIS Center’s

definitions of these indices are reported below:

1- Risk of Expropriation: This variable evaluates the risk of outright

confiscation and forced nationalization of property. Lower ratings are given to

countries where expropriation of private foreign investment is a likely event (Knack,

Stephen [principal investigator(s)] / PRS Group [distributor], 1982-1997).

2- Corruption: Lower scores indicate that high government officials are likely

to demand special payments and that illegal payments are generally expected

throughout lower levels of government in the form of bribes connected with import

' List o f developed (OECD) countries: Australia, Austria, Canada, Denmark, Finland,France, Germany, Greece, Ireland, Italy, Japan, Korea, M exico, Netherlands, N ew Zealand, Norway, Portugal, Spain, Sweden, Turkey, UK, and U SA .2 List o f developing countries: Argentina, B olivia, Chile, Colombia, Ecuador, Guatemala, Honduras, India, Iran, Kenya, M alawi, M orocco, Panama, Peru, Philippines, and V enezuela.

46


and export licenses, exchange controls, tax assessment, police protection, or loans

(Knack, Stephen [principal investigator(s)]/'PRS Group [distributor], 1982-1997).

From the definitions above, it can be seen that the two indices are closely

related. There may be measurement error in each individual index, and taking the

simple average of the two yields a better estimate of the determinants of the

confiscatory tax imposed by corrupt government officials. I will label the average of

the two indices the Expropriation Index (El), where the higher the El the lower the

incidence of corruption and risk of expropriation.

2.3.2. Value added data for 28 three-digit ISIC manufacturing aggregates were drawn

from the UNIDO INDSTAT3 database, available from the United Nations. The

dependent variable (value-added share of the relatively capital-intensive industries to

the value-added share of the relatively labor-intensive industries) used in the panel

data regressions below, was constructed by dividing the total value added output of

the 14 most capital-intensive industries by the total value added output of the 14 most

labor-intensive industries. Classification of labor-intensive and capital-intensive

industries wwas done in accordance with Schott [2001], where sectors were ordered

in terms of increasing capital intensity according to maximum observed value added

per worker.

Capital Stock per worker data in 1985 prices were collected from version 5.6

of the Penn World Table. The Penn World Table displays a set of national accounts

economic time series covering many countries. Its expenditure entries are

denominated in a common set of prices in a common currency so that real quantity

47


comparisons can be made, both between countries and over time. The table also

provides information about relative prices within and between countries, as well as

demographic data and capital stock estimates.

Gross enrollment ratios for primary, secondary and tertiary levels of education

were collected from the UNESCO Institute for Statistics. Total enrollment in a

specific level of education, regardless of age, is expressed as a percentage of the

official school-age population corresponding to the same level of education in a given

school-year.

Finally, oil production data were collected from the CIA World Factbook.

The data are used to construct a dummy variable which takes on a value of 1 for a

country if it is one of the top 30 oil producing nations or a 0 if it is not.

2.4 Empirical Results

In this section we use panel data for 22 developed (OECD) and 16 developing

countries to test the relationship between capital stock per worker and the ratio of the

value-added share of the relatively capital-intensive industries to the value-added

share of the relatively labor-intensive industries. Subsection 2.4.1 focuses on OECD

countries where I find a positive and statistically significant relationship between

capital stock per worker and the ratio of the value-added share of the relatively

capital-intensive industries to the value-added share of the relatively labor-intensive

industries. The relationship remains positive and statistically significant even after

controlling for the expropriation index, education index and the oil dummy variable.

Subsection 2.4.2 focuses on developing countries where I find a negative and not

48




share of the relatively labor-intensive industries. The relationship remains negative

and not statistically significant even after controlling for the expropriation index,

education index and the oil dummy variable.

To test my hypothesis I use panel data regressions. Below is the regression

equation for my estimation:

LN(C, / Z.) = a + fi lLN(Ki /L ,) + fi2LN(EI i) + fi-iLN(OILi) + fiALN(EDUi) + u, ,

where C / L represents the ratio of the value-added share of the relatively capital-

intensive industries to the value-added share of the relatively labor-intensive

industries, K / L represents capital stock per worker, El represents the risk of

expropriation index, OIL represents the oil production index and EDU represents

the level of education index.

2.4.1. OECD Countries - In Table 2.2 below, we report our results from estimating

the Rybczynski effects for a sample of 22 OECD countries using both fixed-effects

and random-effects methods. The results are similar between the two methods. The

Hausman test supports the hypothesis of no correlation between the independent

variables and the country specific effects, so the random-effects estimator is valid.

Table 2.2 shows that there is a positive and statistically significant relationship

between capital stock per worker and the dependent variable (ratio of the value-added

share of the relatively capital-intensive industries to the value-added share of the

relatively labor-intensive industries), both in the random-effects and fixed-effects

49


methods. Controlling for the risk of expropriation (expropriation index), I find a

positive and statistically significant relationship between both independent variables

(capital stock per worker and the expropriation index) and the dependent variable

(ratio of the value-added share of the relatively capital-intensive industries to the

value-added share of the relatively labor-intensive industries). Overall the R-square

increases from 0.346 to 0.415 for the random effects model and from 0.346 to 0.427

for the fixed effects model. The increase in the R-square implies that the

expropriation index plays an important role in explaining variations in the ratio of the


share of the relatively labor-intensive industries.

Controlling for the level of education (education index), oil production (oil

dummy variable) and risk of expropriation (expropriation index) we find a not

statistically significant relationships between two independent variables (the

education index and the oil dummy variable) and the dependent variable (ratio of the


share of the relatively labor-intensive industries), while the relationships between the

remaining two independent variables (capital stock per worker and the expropriation

index) and the dependent variable (ratio of the value-added share of the relatively


industries) remain positive and statistically significant.

50


Table 2.2Estimating Rybczynski effects for a sample of 22 OECD Countries

Dependent variable: LN(value-added share o f the relatively capital-intensive industries / value-added share o f the relatively labor-intensive industries)

Independentvariable (1) (2) (3) (4) (5) (6) (7) (8)

Constant -0 .618 -0 .317 -0 .502 -0 .172 -0.502 -0 .172 -0 .613 -0 .328LN(Capital stock per worker)

0 .260(0 .071)***

0 .192(0 .078)**

0.183(0 .077)**

0.1124(0 .084)

0 .180(0.077)**

0.1124(0 .084)

0 .186(0 .103)*

0.101(0 .113)

LN(Expropriation Index)

0 .240(0 .091)***

0.224(0 .091)**

0.239(0 .091)***

0.224(0 .091)**

0 .220(0 .097)**

0 .206(0 .097)**

Oil(OIL)

0.0567(0 .077)

0 .056(0 .079)

--------

LN(Education)

0 .056(0 .258)

0 .116(0 .266)

R 2 0 .346 0 .346 0.415 0 .427 0.401 0 .427 0 .374 0 .406

Number o f observations

175 175 175 175 175 175 165 165

Estimationmethod

Randomeffects

Fixedeffects

Randomeffects

Fixedeffects

Randomeffects

Fixedeffects

Randomeffects

Fixedeffects

Hausman Test (Prob.Rejecting Ho)

0.0392 0.5886 0.7281 0 .9739

*** = significant at the 0.01 level, * = significant at the 0.10 level** = significant at the 0.05 level, Standard error in parenthesisHo (Hausman Test): Difference in coefficients not systematic

Overall the R-square drops from 0.415 to 0.374 for the random effects model and

from 0.427 to 0.406 for the fixed effects model.

2.4.2. Developing Countries — In Table 2.3 below, we report our results from

estimating Rybczynski effects for a sample of 16 developing countries using both

fixed-effects and random-effects methods. The results are similar between the two

methods. The Hausman test supports the hypothesis of no correlation between the

51


independent variables and the country specific effects in almost all cases, so the

random-effects estimator is valid. Table 2.3 shows that there is a negative and not



share of the relatively labor-intensive industries, both in the random-effects and fixed-

effects methods. Controlling for the risk of expropriation (expropriation index), I find

a positive and statistically significant relationship between the expropriation index

and the dependent variable (ratio of the value-added share of the relatively capital-

intensive industries to the value-added share of the relatively labor-intensive

industries) while a negative and not statistically significant relationship maintains

between capital stock per worker and the dependent variable. Overall R-square

increases from 0.006 to 0.011 for the random effects model and from 0.006 to 0.018

for the fixed effects model. The significant increase in R-square implies that the

expropriation index plays a very important role in explaining the variation in the ratio

of the value-added share of the relatively capital-intensive industries to the value-

added share of the relatively labor-intensive industries. The low level of R-square

with capital stock per worker as the only independent variable implies that capital

stock per worker plays a minor role in explaining variations in the ratio of the value-

added share of the relatively capital-intensive industries to the value-added share of

the relatively labor-intensive industries.

Controlling for the level of education (education index), oil production (oil

dummy variable) and risk of expropriation (expropriation index) we find not

statistically significant relationships between three independent variables (capital

52


stock per worker, the education index and the oil dummy variable) and the dependent

variable (ratio of the value-added share of the relatively capital-intensive industries to

the value-added share of the relatively labor-intensive

Table 2.3Estimating Rybczynski effects for a sample o f 16 developing countries

Dependent variable: LN(value-added share o f the relatively capital-intensive industries / value-added share o f the relatively labor-intensive industries)

Independentvariable (1) (2) (3) (4) (5) (6) (7) (8)

Constant 0 .514 0.558 0.292 -0 .208 0.146 -0 .208 0.262 0 .329LN(Capital stock per worker)

-0 .030(0 .069)

-0.041(0 .190)

-0 .006(0 .071)

0 .116(0 .197)

0 .040(0 .081)

0 .116(0 .197)

0.051(0 .103)

0 .155(0 .228)

LN(Expropriation Index)

0.201(0 .099)**

0.265(0 .108)**

0 .210(0 .099)**

0 .265(0 .108)**

0 .154(0 .115)

0 .230(0 .127)*

Oil(OIL)

-0 .097(0 .081)

. --------------------- -0 .101(0 .086)

---------------------

LN(Education)

-0 .067(0 .341)

-0 .370(0 .442)

R 2 0 .006 0 .006 0.011 0.018 0.023 0.018 0 .030 0 .059

Number o f observations

127 127 127 127 127 127 106 106

Estimationmethod

Randomeffects

Fixedeffects

Randomeffects

Fixedeffects

Randomeffects

Fixedeffects

Randomeffects

Fixedeffects

Hausman Test (Prob.Rejecting Ho)

0.9492 0.2472 0.3239 0.4065

*** = significant at the 0.01 level, * = significant at the 0.10 level** = significant at the 0.05 level, Standard error in parenthesisHo (Hausman Test): Difference in coefficients not systematic

industries) while the relationship between the expropriation index and the dependent

variable remains positive and statistically significant in the fixed-effects method.

Overall R-square increases from 0.018 to 0.059 for the random effects model and

from 0.011 to 0.030 for the fixed effects model. The increase in R-square implies that

the education level plays an important role in explaining variations in the ratio of the


share of the relatively labor-intensive industries.

53


Results from the panel data regressions are consistent with the theoretical

results obtained in the analytical section of the paper. Controlling for the level of

education (education index), oil production (oil dummy variable) and risk of

expropriation (expropriation index), a not statistically significant relationship obtains

between capital stock per worker and the dependent variable (value-added share of

the relatively capital-intensive industries to the value-added share of the relatively

labor-intensive industries) for a sample of 16 developing countries while a positive

and statistically significant relationship obtains between capital stock per worker and

the dependent variable (value-added share of the relatively capital-intensive industries

to the value- added share of the relatively labor-intensive industries) for a sample of

22 developed (OECD) countries. The not statistically significant relationship

obtained for the 16 developing countries implies a statistically not significant rate of

change in the ratio of capital-intensive output to labor intensive output caused by a

change in the capital stock per worker, while the statistically significant relationship

obtained for the 22 developed countries implies a positive and significant rate of

change in the ratio of capital intensive output to labor intensive output caused by a

change in the capital stock per worker.

The positive and statistically significant relationship between the

expropriation index and the dependent variable (ratio of the value-added share of the

relatively capital- intensive industries to the value-added share of the relatively labor-

intensive industries) for both developed and developing countries implies that risk of

expropriation in a country plays a significant role in explaining the variation in the

54


ratio of the value-added share of the relatively capital-intensive industries to the

value-added share of the relatively labor-intensive industries.

Finally we conduct robustness checks regarding our measures of industry

classification and our measures of education level. To check our measure of industry

classification, we ran panel data regressions using the eight most factor intensive

industries instead of the 14 most factor intensive industries used in our analysis

above.

Our results did not change qualitatively. For developing countries, the

relationship between capital stock per worker and the dependent variable (ratio of the


share of the relatively labor-intensive industries) remained negative and statistically

not significant while the relationship between the expropriation index and the

dependent variable (ratio of the value-added share of the relatively capital-intensive

industries to the value-added share of the relatively labor-intensive industries),

remained positive and statistically significant. For OECD countries, the relationship

between both independent variables (capital stock per worker and the expropriation



industries) remained positive and statistically significant.

To check our measure of education level, we ran panel data regressions using

separate gross enrolment ratios for each of the primary, secondary and tertiary levels

of education. Our results did not change qualitatively. For developing countries, the

relationship between capital stock per worker and the dependent variable (ratio of the

55



share of the relatively labor-intensive industries) remained negative and statistically

not significant while the relationship between the expropriation index and the

dependent variable (ratio of the value-added share of the relatively capital-intensive

industries to the value-added share of the relatively labor-intensive industries),

remained positive and statistically significant. For OECD countries, the relationship

between both independent variables (capital stock per worker and the expropriation



industries) remained positive and statistically significant. So we can conclude that

our panel data regressions results are robust to changes in both our measures of

industry classification and education level.

2.5 Concluding Remarks

From our model developed above, we were able to provide an explanation for cross

country differences in the ratio of capital-intensive output to labor intensive output

(for countries with similar capital stock per worker). We were also able to provide an

explanation as to why certain developing countries (higher incidence of corruption

and higher risk of expropriation) are slower in climbing the ladder of comparative

advantage that a country will climb as it accumulates capital relative to the world. In

the second part of the paper we used a sample of 16 developing countries, 28

manufacturing industries and eight years, to find evidence contradicting the

predictions of Rybczynski theorem. Our empirical findings suggest that Rybczynski

56


predictions could seize to hold in countries with high incidence of corruption and

high risk of expropriation. It is important to mention that the model developed in this

paper is intended to explain cross country differences in the ratio of capital-intensive

output to labor intensive output and is not intended to explain the contradiction in the

predictions of Rybczynski theorem arri ved at in the empirical part of the paper.

57


Chapter 3

Contests with a Generalized Difference Form*

3.1 Introduction

The literature on rent- seeking games has expanded quite rapidly in the past two

decades. According to Anderton (2001), one of the necessary building blocks of a

unifying micro-theory of conflict economics is the contest success function (CSF),

which specifies how the appropriative efforts of agents lead to an appropriative

outcome. To date, two families of CSFs have been developed. The first family of the

CSF comes from the Tullock (1980) rent-seeking game in which a contestant’s

winning probability depends on the ratio of fighting efforts. In the second family of

success functions, called “ difference-form” success functions, a contestant’s

probability of winning depends upon the difference of fighting efforts (Hirshleifer

1995).

The game-theoretic rent-seeking model studied by Tullock (1980) marked a

starting point for numerous studies on the subject. Perez-Castrillo and Verdier (1992)

stressed the importance of the shape of the players’ reaction curve in order to

* This chapter is co-authored with Stergios Skaperdas.

58


understand the impact of the technology4 of rent-seeking on the structure of the

outcome of the game. Their findings indicate that, in the case when the rent-seeking

technology displays constant or decreasing returns to scale5, the reaction curve of the

agent is continuous in the bets of the other agents, increasing at first when the outside

competition is weak and decreasing continuously as the outside competition

increases. In the case of increasing returns to scale, a sharp discontinuity in the

reaction curve obtains. This discontinuity is essentially due to the nonconvexity of

the profit function of the agent. Based on the type of technology of rent-seeking, the

authors also characterize the type of pure strategy equilibria that can result in the

game. With constant or decreasing returns to scale and for a fixed number of agents,

there exists a unique Nash equilibrium which is symmetric. With increasing returns

to scale, if the number of agents is not too large, there also exists a unique symmetric

Nash equilibrium. However, if the number of agents is too large, then there exists a

multiplicity of equilibria, which are asymmetric with some agents devoting the same

amount of resources to rent-seeking and the remaining agents remain inactive.

Nitzan (1994) surveys alternative ways of modeling rent seeking contests,

focusing primarily on the relationship between the extent of rent dissipation6 and the

underlying contest characteristics: for example the number of players, the degree of

4 Following Tullock (1980) contestant i ’s probability o f winning a contested prize isN

P j = e ' ! { e \ + , w hen contestants) = 1, ,N expend “effort” C - > 0 . A ccording to Perez-7=1j * i

Castrillo and Verdier (1992), r > 0 characterizes the returns o f scale o f the technology o f rent- seeking.5 When r < 1 the technology o f rent-seeking may be considered with decreasing returns o f scale while when r > 1 the technology is with increasing returns.6 Rent dissipation is defined as the ratio between total rent-seeking outlays in equilibrium and the value o f the contested rent.

59


asymmetry between the players, and the nature and source of the rent. He showed that

the extent of rent dissipation is increasing in the number of rent seekers and in the

marginal return to lobbying outlays.

Hirshleifer (1989), studied difference-form contests with two contestants,

obtaining results that are different from those of the Tullock game. Hirshleifer

pointed out that a crucial flaw of the traditional ratio model is that neither one-sided

submission nor two-sided peace between the parties can ever occur as a Cournot

equilibrium. In contrast, both of these outcomes are entirely consistent with a model

in which success is a function of the difference between the parties' resource

commitments. Che and Gale (2000) characterized equilibria for all parameter values

for a particular class of difference-form contest success function, namely the

piecewise linear function. In their work, they find similarities between general

difference-form contests and all-pay auctions.

Skaperdas and Vaidya (2005) propose a general class of “difference-form”

contests for settings in which rent-seeking involves persuasion. Examples of such

settings include litigation, advertising, lobbying, electoral campaigning or

argumentation in policy debates where contending parties expend resources to

persuade an audience of the correctness of their view. They examine how the

probability of persuading the audience depends on the resources expended by the

parties, so that persuasion can be modeled as a contest. In the present work we

attempt to explore the properties and implications of the functional form proposed by

Skaperdas and Vaidya (2005) by providing a complete characterization of the

players’ reaction functions and the pure strategy equilibria. We also discuss the

60



characteristics: the nature of the contested rent, the number of players, the cost per

unit of persuasion activity, and the force of the evidence.

Our results for the case of two players show that when the persuasion function

is symmetric, the reaction curve of each agent is independent of the efforts of the

other agent and the non-cooperative (persuasion) equilibrium is symmetric in the

equilibrium efforts expended by both agents. Moving to more complicated cases with

asymmetric cost functions and asymmetric contestable rents, the non-cooperative

persuasion equilibrium is asymmetric in the equilibrium efforts expended by both

agents. The agent with the relatively lower cost of persuasion per unit of her

valuation of the contestable rent expends greater effort in equilibrium. The increase

in the agent’s equilibrium effort is due to the concavity of the evidence production

function and to the decrease in her marginal cost relative to the marginal cost of the

other agent. With asymmetric evidence production functions, the non-cooperative

persuasion equilibrium is also asymmetric in the equilibrium efforts expended by

both agents, with the agent on the side of the truth expending greater persuasion effort

in equilibrium. In this case, the agent’s greater equilibrium persuasion effort is due to

the increase in her relative advantage in the production of evidence at the margin.

We also characterize the type of pure strategy equilibria that may result in the

game. First we discuss the case where the total number of agents potentially

interested in persuasion is fixed to some number, which can exceed 2, and the

persuasion function is symmetric. If the number of agents is such that the positive

profits condition is satisfied then there exists a unique Nash Equilibrium which is

61


symmetric. However, if the number of agents is too large and the positive profits

condition is no longer satisfied, then there exists a multiplicity of equilibria, which

are asymmetric. Some agents devote the same amount of resources to persuasion and

the remaining agents choose not to participate. In contrast to the literature surveyed

by Nitzan (1994), we show that the extent of rent dissipation is non-monotonic in the

number of rent seekers N. We also show that the extent of rent dissipation is non

monotonic in the contestable rent and in the cost per unit of persuasion activity while

increasing in the force of the evidence presented to a third party audience. The

greater the force of the evidence presented to the third party audience, the greater the

return to the resource investment by both contestants and the higher is the amount of

persuasion effort expended by all parties in equilibrium.

Finally we examine the case when the persuasion function is asymmetric. Our

results show that the reaction curve of our agent is determined by the amount of effort

expended by the other agent and by the degree of asymmetry between the likelihood

ratios of judgment held by the third party audience. The reaction curve of each agent

is continuous in the efforts of the other agent with the reaction curve of the favored

agent increasing continuously as the outside competition increases while the reaction

curve of the other agent decreases continuously as the outside competition increases.

The paper is organized as follows. Section 2 describes an alternative to the

Tullock functional form proposed by Skaperdas and Vaidya (2005). Section 3

outlines the model under symmetry and characterizes the non-cooperative pure

strategy equilibrium with two agents. Sections 4 through 8 focus on the symmetric

7 One agent is favored in terms o f the force o f the evidence presented to the third party audience and in terms o f the negative bias in judgm ent b y the third party audience.

62


case and characterize: the non-cooperative pure-strategy equilibrium with asymmetric

cost functions and asymmetric contestable rents, the non-cooperative persuasion

equilibrium with asymmetric evidence production functions, the non-cooperative pure

strategy equilibria with N agents, persuasion with a fixed number of agents N, and the


characteristics. Section 9 examines the non-cooperative persuasion equilibrium with

asymmetry. Section 10 concludes.

3.2 Persuasion Function as an Alternative to the Tullock

Functional Form

To lay out the building blocks of persuasion, Skaperdas and Vaidya (2005) examine

an evidence production process. Two players, player 1 and player 2, compete to

gather and present evidence so as to influence the verdict of a third party audience in

their favor. With discrete evidence production, Player 1 can either produce evidence

in her favor denoted by Ex, or offer no evidence, denoted by { }. Similarly, Player 2

can either produce evidence in her favor, denoted by E2, or offer no evidence, { }.

The production of such evidence is not deterministic. The amount of resources

enhances the probability of finding a favorable piece of evidence. The authors let

h(r}) denote the probability that player 1 will find evidence in her favor. This

probability is increasing in rx, the resources expended on finding that evidence.

Similarly h(r2) denotes the probability that player 2 will find evidence in her favor,

with that probability also increasing in the resources r2 expended by the player. Thus

63


in terms of evidence there are four possible states of the world that can be faced by

the third party audience: (EX,E2),(EX,{ }),({ },E2),and({ },{ }) occurring with the

following probabilities: h(rx )h{r2), h(rx )[1 - h(r2)], [1 - h{rx )]h(r2), and

[1 - h(rx )][1 - h(r2)] respectively. Given the posterior probability of player 1 winning

(and of player 2 losing) that will be induced by each realized combination of evidence

and given the function h(.), the ex ante probability of player 1 winning (and of player

2 losing) can be straightforwardly calculated:

where n represents the third party audience’s posterior probability of winning for

player 1 and n represents the third party audience’s prior. T and 6 are defined

according to the restrictions below:

P\ Oi,r2) = Krx)h(r2 (Ex, E2) + h(rx)[1 - h(r2)]x*(Ex,{ })

+ [1 - h ( r xm r 2) n \ { },E2) + [1 - h{rx)}[\ - h{r2)}n ({ },{ })(1)

Equation (1) above can be rearranged as:

Pl(rx,r2) = n + n[(T- 1)h(rx)-(1 - S)h(r2)] + [n (Ex,E2) + (1 - S - T)jc]h(r,)h(r2) (2)

n (<(), (j)) = k \ (3)

n (ff),E2) = 8n for some 8 e (0,1);

whereT > 1

Skaperdas and Vaidya (2005) also examine equation (2) above in the case

with symmetry when a = l - S = T - 1 , 7r*(j>,fi) = 7t*(Ex,E2) = 7r, and n

probability that player 1 wins then takes the following simple form:

64


P\(rv ri) ~ n +om[h(r]) - h ( r 2)] 1 > a > 0, (4)

where rx, r2, and h{.) are as defined above, a represents the force of the evidence

(the higher is the force of the evidence the higher is the contestant’s probability of

winning the contest).

3.3 The symmetric case

Using the symmetric form of the persuasion function that was derived in Skaperdas

and Vaidya (2005) and explained in section 2 above, we consider the basic rent-

seeking contest with 2 contending parties confronting the opportunity of winning a

fixed prize, the contestable rent, X . The contending parties expend resources to

persuade a third party audience of the correctness of their view. The probability of

persuading the audience depends on the resources expended by the parties so that the

probability that agent 1 wins takes the simple form:

where the parameter a and the probability function h(r) are as defined in equation

(4) above. We also make the following assumptioms:

(5)

h :U c: 91 —» 91 is C2 ,i.e. h is continuous with h (r) < 0 for all r e U .

The expected profit of agent 1 can then be written as:

V' (r,) = ! i + a i [A(r,) - H r , )] }X - cr, (6)

65


where c represents the cost per unit of persuasion activity and X , as previously

defined, represents the contestable rent. The agent’s decision problem then becomes

to maximize her expected profit V 1 taken r2 as given and under the constraint r > 0 .

The first order condition, at an interior optimum yields:

n = < i > Y A (7)a X

We note that r* represents the optimal effort chosen by agent 1. Proposition

1 below characterizes her best response function:

Proposition 1

Two cases are possible:

For 0 < r2 < G(c ,a ,X) , r* is strictly positive for and determined by the first order

condition (7).

For r2 > G(c,a ,X) , r*= 0.

where G(c, a, X ) =hTx[h{r\)Jt - ----- —— r,*] and h \ r ) < 0.a a X

Proof: See Appendix.

Proposition 1 states, player 1 will choose to invest in persuasion activities

determined by the first order condition (7) only if the persuasion effort exerted by

player 2, r2, is less than a certain level given by G(c ,a ,X ). If player 2 chooses a

greater level of effort, r2 > G (c ,a ,X ) , player 1 will choose not to participate in

persuasion activities and her best response function r* equals zero. The point

G(c,a ,X) marks the point of complete dissipation of the rents.

66


From Proposition 1, we can see the shape of the reaction function r *, as

illustrated in Figure 3.1 below. As Figure 3.1 shows, the best response of player 1 r*

falls discontinuously from a positive value determined by the first order condition (7)

to zero as the effort exerted by the other player r2, passes through the threshold value

of G(c,a ,X) .

K

F ig , 3. J Player 1 rs reaction curve

Proposition 2

A multiplicity of Nash equilibria are possible in this case. One possible Nash

equilibrium is such that both agents invest the same amount of persuasion effort r* in

persuasion given by equation (7) above. A second possible Nash equilibrium is such

that both agents invest zero persuasion effort in persuasion.

67


A necessary condition for the existence of the first Nash equilibrium (where

« Xboth agents invest the same amount of persuasion effort r ) is that < — and

2c

* Xr2 < — . The equilibrium expected profit of agent 1 involved in persuasion is then:

2c

K = l \ x + ~ X h ( r ; ) - ~ X h(r;)]-cr; (8)

V ' X x - c r (9)

while agent 2’s expected profit takes the following form:

v;=[±x+jXh(r;)-~xh(r;)]-Cr; m

V2* = l x - c r * (11)


Figure 3.2 below maps a possible Nash equilibrium of the 2-player game

described in proposition 2 above. We can see from the figure that the total cost of

persuasion effort expended in equilibrium 2 cr* cannot exceed the amount of the

contestable rent X .

68


*

X2c ■ 2

F ig , 3 .2 Non-cooperative pure strategy equilibrium

The analysis in sections 4 though 8 below will focus on the symmetric case

discussed above. Section 9 will examine the non-cooperative persuasion equilibrium

with asymmetry when 1 - 6 ^ T -1 and n *(<!>, (/>) * n*(Ev E2) .

3.4 Non-cooperative equilibrium with asymmetric cost

functions and asymmetric contestable rents

We consider the case with two agents under asymmetric cost structures. Agent 1 ’s

cost function is C, (r,) = c,r\ while agent 2’s cost function is C2 (r2) = c2r2 with

Cj ^ c'2 • We will also consider that agent 1 ’s interpretation of the contestable rent X

69


differs from agent 2’s and are given as X ] and X 2 respectively. The expected profit

of agent 1 may be then written as:

>/V,) = <i + f [A(r,)-A(r2)]}.r, - c , ,„ (12)

where agent’s 1 decision problem is to maximize her expected profit V 1 taking r2 as

given and under the constraint r > 0 . The first order condition yields:

r,'=(A')-,(J^ -) , 03)a X x

We note that represents the optimal effort chosen by agent 1. Similarly for

agent 2:

(14)a X 2

Proposition 3


equilibrium is such that the 2 agents invest different amounts of persuasion effort

given by their optimal efforts in equations (13) and (14) above. A second possible

Nash equilibrium is such that one agent exerts zero effort while the second agent

exerts positive effort given by her first order condition in equations (13) or (14)

above. The third possible Nash equilibrium is such that both agents invest zero

persuasion effort.

Necessary conditions for the existence o f such equilibria are

70


] which ensures

V'x , F2* > 0. The equilibrium expected profits to each agent involved in persuasion

are:


Figure 3.3 below maps one possible Nash equilibrium of the 2-player game

described in proposition 3 above. The non-cooperative persuasion equilibrium is

asymmetric in the equilibrium efforts expended by both agents. The agent with the

relatively lower cost of persuasion per unit of her own interpretation of the

contestable rent expends greater persuasion effort in equilibrium.

V* = ^ - [ l + a h(r*) - a h{r *)] - c,r/ (15)

(16)

71


c cF ig , 3 ,3 Non-cooperative pure strategy equilibria -

3.5 Non-cooperative equilibrium - with asymmetric

evidence production functions

We examine a setting where two players, player 1 and player 2, compete to gather

and present evidence so as to influence the verdict of a third party audience in their

favor. When player 1 is on the side of the truth, evidence production by player 1 and

player 2 can be determined by the following functions:

e, = 6 h{rx) (17)

e 2 = 0 -6 )A (r2) (18)

where,

72


- < 9 < 1 (19)2

where e, and e2 represent evidence production for player 1 and player 2 respectively.

The function /?(.) is as defined in (5) above while the parameter 6 captures the fact

that the truth does matter in the production of evidence. Given, for example, that

6 >1/2, if both parties devoted an equal amount of effort to gather and present

evidence to the court, the outcome would favor player 1.

The expected profit to player 1 may be then written as:

V'' (r, ) = { + j [e Hr, ) - (1 - 6 ) h(n)] }X - cr,, (20)

where player 1 ’s decision problem is to maximize her expected payoff F 1 taking

r2 > 0 as given and under the constraint rx > 0. The first order condition yields:

(21)aO X

We note that r * represents the optimal effort chosen by player 1. Similarly

for player 2:

(22)

Proposition 4


equilibrium is such that the 2 agents invest different amounts of persuasion efforts

given by their optimal efforts in equations (21) and (22) above. A second possible

Nash equilibrium is such that one agent exerts zero effort while the second agent

exerts positive effort given by her first order condition in equations (21) or (22)

73


above. The third possible Nash equilibrium is such that both agents invest zero

persuasion effort in persuasion. The parameter 6 captures the fact that the truth does

matter in the production of evidence with player 1 being favored in this case.

Necessary conditions for the existence of such equilibrium are

r; <[gh(r; ) - ( \ - e ) h ( r;) + - \ [ C \ and r2* < [ 0 - e)ACr2")- 6>A(V> + —a 2c a 2c

which ensures F,*, V*2 > 0. The equilibrium expected profits to each agent involved

in persuasion are:

K =[^x+^exh(r;)~(\~e)x h(r;)\-cr; (23)

K = l ^ X + 0 X H r ; ) - ^ ( l - 0 ) X h ( r ; ) ] - cr; (24)


Figure 3.4 below maps a possible Nash equilibrium of the 2-player game

described in proposition 4 above. The non-cooperative persuasion equilibrium is

asymmetric in the equilibrium efforts expended by both players with the player on the

side of the truth expending greater persuasion effort in equilibrium. The increase in

the equilibrium persuasion effort exerted by the player is due to the increase in her

marginal benefit relative to the marginal benefit of the other player.

74


1 CY. X[(1 - & ) k ( r ' ) - d h ( ^ ) + — ][—

a 2 c

F ig , 3 ,4 Non-cooperative pin e strategy equilibria - (l - &) < &

3.6 Non-cooperative pure strategy equilibria with N agents

With N contending parties confronting the opportunity of winning a fixed prize X ,

we conjecture that the probability that agent i wins depends on the difference between

her effort, rt , and the mean value of the efforts expended by all other agents, r . ,

j ^ i and it takes the following form:

7=1i*jN ~ 1

(25)

h{.) is increasing in r and the other variables and functions are similarly

defined to those in (5). The expected profit of agent i may be then written as:

75


Where the agent’s decision problem is to maximize her expected profit V

taking the effort exerted by other agents r . , j i as given and under the constraint

r . > 0 . The first order condition yields the optimal persuasion effort chosen by agent

Proposition 5 below characterizes agent i’s best response function:

Proposition 5

Two cases are possible:

For r < G ( N , c , a , X ) , then r* is strictly positive for ry >0 and determined by the

first order condition (27).

For r > G( N, c ,a , X) , then r*= 0.


Proposition 6

Nash equilibria with N agents are such that all agents invest the same amount

of persuasion effort r in persuasion. One possible Nash equilibrium is such that all

i :

(27)

where G(N, c ,a , X) =h l [h(r*)+-

76


agents invest the same amount of effort given by equation (27) above. The other

possible Nash equilibrium is such that all agents invest zero effort.

XA necessary condition for the existence of such an equilibrium is r < ----- .

N c

The equilibrium expected profit to each agent involved in persuasion is:

V* = [ ^ + ^ h ( r * ) - — h(r*)]-cr* (28)N N N

V* = - - c r * (29)N


Similar to section 3 above, the total cost of persuasion effort expended in

equilibrium N cr* cannot exceed the amount of contestable rent X .

3.7 Persuasion with a fixed number of agents N

In this section we discuss how the total number of agents N(> 2) potentially

interested in persuasion can affect the symmetry of the Nash equilibrium in pure

strategies.

Proposition 7

Two cases are possible.

a. If — > N(h (-^-^-) > 0 , then there is a unique Nash equilibrium in which all thec a X

N agents participate in persuasion activity with each of them investing

77


N cr - (h y l (----- ) . The equilibrium expected profit for each agent is equal toa X

v‘ =^--(c)(h'r'A> o.N a X

b. If — < N(h y ' ( - ^ - ) , let N* be the highest number of agents such that c a X

— > N(h')~x ( - ^ - ) > 0. Then if N* > 1, the Nash equilibria in pure strategies are c a X

asymmetric. There exists an equilibrium with N* agents participating in persuasion

activity and N - N * non-participating agents in which each of the participating

* - _ t N Cagents devotes r - (h y (----- ) of resources to persuasion and receives a profita X

* X . N cV (c)(h ) (----- ) > 0. Each of the non-participating agents invests nothingN a X

and has a zero payoff.

3.8 Non-cooperative equilibrium and the extent of rent

dissipation

The existing rent-seeking literature is concerned with the existence and

characterization of Nash-equilibria and, in particular, with the relationship between

total rent-seeking outlays in equilibrium and the value of the contested rent. The ratio

D between these two values is called the extent of rent dissipation. This ratio is

important, as it measures the resources squandered on the contested rent from its

value [Nitzan (1994)]. Our results show that the extent of rent dissipation is non-

78


monotonic in the number of agents N, while in the case of the Tullock function it is

strictly increasing in N.

Proposition 8

When the probabilistic contest success functions are symmetric and of the

form shown in (27) and if an interior Nash equilibrium in pure strategies exists, then

N c . N cthe extent of rent dissipation D = ( )(h ) ( ) < 1. The extent of rent

X cc X

N cdissipation can be decomposed into two multiplicative parts:---- which represents

X

, N cthe total cost of persuasion activity per unit of the contestable rent and (h ) (----- )

a X

which represents the symmetric equilibrium effort (see equation (27)). The extent of

rent dissipation is non-monotonic in the contestable rent X , in the number of rent

seekers N and in the cost per unit of persuasion activity c while increasing in the

parameter a . The extent of rent dissipation is increasing in the number of agents N

and in the cost per unit of persuasion activity c when the symmetric equilibrium effort

is decreasing at a slower rate than the rate of increase in the total cost of persuasion

activity per unit of the contestable rent — and — respectively. Conversely the extentN c

of rent dissipation is decreasing in the contestable rent X when the symmetric

equilibrium effort is decreasing at a faster rate than the rate of decrease in the total

cost of persuasion activity per unit of the contestable rent - — . The parameter aX

represents the force of the evidence (the higher is a the higher is the contestant’s

probability of winning the contest). So the higher the a , the greater the return to the

79


resource investment by both contestants and the higher is the amount of persuasion

effort expended by all parties in equilibrium.


In the appendix, we show that when the rate of decrease in the symmetric

cost of persuasion activity per unit of the contestable rent — then the extent of rent

dissipation D is increasing in the number of agents N and decreasing otherwise.

From a more technical viewpoint, A is a measure of the degree of concavity of the

probability function h( .) . It measures the speed at which the marginal probability of

finding evidence in the agent’s favor is decreasing. When the marginal probability of

finding evidence in the agent’s favor is decreasing at a slower rate than the rate of

increase in the total cost of persuasion activity per unit of the contestable rent ,

then the extent of rent dissipation, D , is increasing in the number of agents N ,

otherwise, it is decreasing in N . A similar relationship can be established between

the cost per unit of persuasion activity c and the extent of rent dissipation D while a

converse relationship can be established between the contestable rent X and the

extent of rent dissipation D.

3.9 Non-cooperative equilibrium - asymmetric case

dj h ' y1 N cdN a X )

equilibrium effort A - - is less than the rate of increase in the total

80


With asymmetry, the probability that agent 1 wins takes the following functional

form:

p x(rx,r2) = n + n [(T -1 )h{rx) - (1 - 6 )h(r2)]

+ [x* (Ex, E2) + (1 - S - T)x]h(rx )h(r2),

while agent 2’s probability takes the following form:

p 2^ , r 2) = \ - n + n [ ( l - m r 2) - ( r - m r , ) ]

+ [(<5 + r - \ )x - x \ E x,E2)]h(rx)h(r2),

where T, 6, n and h(.) are as defined in (2) and (3) above. The expected profit of

agents 1 and 2 may be then written as:

V1 (rx) = {x + 4 r -1 )h(rx) - (1 - S)h(r2)]

+ [x (Ex,E2) + { \ - 5 - T ) x ] h ( r x)h(r2) } X - crx,

V 2(r2) = { l - x + [(1 - S)h(r2) - (T -1 )h(rx)]

- [x (Ex,E2) + ( 1-S - F) x]h{rx)h(r2)}X - cr2,

Here each agent i’s decision problem is to maximize her respective expected profit Vj

taking the resources expended by the other agent as given and under the constraint

rt >0.

The best response of agent 1 to a given effort r2 exerted by agent 2 is:

r; = ( h ' y1 (------------------- ;--------- >, (34)W r-i)i+[/(£1,£2>+(i-j-r>p(/'!)]

Similarly for player 2, we have

r; = ( h ' y x(------------------- ; ), (35)[^(1 - S ) X - [x (Ex, E2) + (1 - 5 - T)x]Xh(rx)]

81


Note that the term [ft* (.£',, /:,) + (1 - 8 - F)/r] is positive providing agent 1

with the advantage in the persuasion contest. We can rewrite the term

[ft* (El ,E1) + ( l - S - T);r] as:

[* ({ },{ } ) - * ( { } ,£ ,) ] - [ * (£ „ { } ) - * (£ „ £ ,) ] (36)

which is positive if the following condition holds:

| * • ( £ „ £ , ) - * • ( £ „ { }) !< | *■•({ } ,£ , ) - » ( { },{ }) | (37)

The above condition is always satisfied since in the early stage of the contest

(when no evidence is presented), the marginal probability increase (that is the extra

contribution) of the evidence E2 presented by agent 2 when no evidence { } has been

presented by agent 1, {ft*({ },E2) ~ ft '({ M }» , is greater than the marginal

probability increase of the same evidence E2 presented by agent 2 when evidence Ex

has already been presented by agent 1, {ft* (Ex, E2) - n* (El , { })}. Proposition 9

below characterizes the agents best response functions:

Proposition 9

The following cases are possible:

r,* is strictly positive and increasing in r2 for r2 >0 and determined by the first-order

condition (34).

For r} < G( c ,X ,n , S , r ) , then r2 is strictly positive and decreasing in r, for r, >0 and

determined by the first order condition (35).

For rx > G(c, X , n , S,T), then r2 = 0.

where G(c,X, f t ,5,T) =h 1 [—----—— ---------------] and h (r)< 0ft (Ex,E2) + ( l - S - T ) f t

82


Nash equilibria are defined at the intersection of r* and r*_


From proposition 9 above, we can see that agent 2 will choose to invest in

persuasion activities determined by the first order condition (35) only if the

persuasion effort rx exerted by agent 1 is less than a certain level given by

G( c , X ,n , S , T ) . For persuasion effort r, greater than G(c,X,n ,6 ,T) , agent 2’s

marginal return to persuasion becomes negative and she will choose not to participate

in persuasion activities with her best response function r*2 being equal to zero.

Proposition 9 defines the Nash equilibria of the 2-player game and it also

defines the shape of the reaction functions r* and r2 • In figure 3.5 below, the Nash

equilibrium of the game occurs at the point of intersection of the two reaction curves

r* and r2 which is indicated by the point of intersection of the two lightly shaded

curves in the middle of the graph. In figure 3.6 below the Nash equilibrium of the

game also occurs at the point of intersection of the two reaction curves >{ and r2*

• cwhich is indicated by the point of intersection (h ) ' (--------------) at the bottom of the[;r(r - \ ) X

graph.

83


r2

Ibts

C r■i7T (Sj.jSj) + (1- 5-r)jr'

Fig. 3,5 Non-cooperative pure strategy' equilibrium - asymmeric example 1

r2

Ib*

T*

C■1n (filt5a)+ ( l-5 - r )? r '

Fig. 3.6 Non-cooperative pure strategy equilibrium - asymmetric example 2

84


Proposition 10

Nash equilibria with 2 agents under asymmetry are such that both agents

invest different amounts of effort r in persuasion. One possible set of Nash

equilibria is such that both agents invest different amount of effort satisfying equation

(38) below. The other possible set of Nash equilibria is such that one agent exerts

zero effort while the second agent exerts positive effort given by the first order

condition (36) above.

i = (38)r2 \ ( T - i ) + [ x \ E , , E 2 ) + ( l - S - r>]ft(r: )

Necessary conditions for the existence of such equilibrium are

, - ir 1 c h(r*) cr, < h [------- 1-----------------;— ------------------- r. 1,1 - S 7C(1-S)X h (r,) 7t(\ - S ) X

, -ir 1 - f t c h(rj) c „ .... .r, < n [------------ 1--------------------r-~----------------- r71. The equilibrium expected

S r (T - l) 7r (T - \ )X h (r2) n ( r ~ \ ) X

profit to each agent involved in persuasion is:

V,‘ = x X + ^ p ± - K ( \ - d ) X h ( r " 2) - c r ; (39)h'{rx )

r ; = ( l - x ) X + ? / ^ ± - x ( r - l ) X h ( r ; ) - c r ; (40)h'(r2)


Our results show that the reaction curve of agent 1 is determined by the

amount of effort expended by agent 2 and by the degree of asymmetry between the

likelihood ratios of judgment held by the third party audience. The reaction curve of

each agent is continuous in the efforts of the other agent with the reaction curve of

85


agent 1 (the agent with the advantage as shown in equations (36) and (37) above)

increasing continuously in the persuasion efforts of agent 2 while the reaction curve

of agent 2 decreases continuously in the persuasion efforts of agent 2.

3.10 Conclusion

In this paper, we have offered a review of the general properties and implications of

the new game-theoretic rent-seeking model proposed by Skaperdas and Vaidya

(2005). We also offered a comparison with the traditional ratio model studied by

Tullock (1980). As argued by Hirshleifer (1989), a crucial flaw of the traditional

ratio model is that neither one-sided submission nor two-sided peace between the

parties can ever occur as a Cournot equilibrium. In contrast, both of these outcomes

are entirely consistent with the new game-theoretic rent-seeking model proposed by

Skaperdas and Vaidya (2005) in which success is a function of the difference between

the parties' resource commitments. We argue that the new proposed functional form

is suitable for a wider range of applications than the traditional ratio model proposed

by Tullock. Examples of such applications include lobbying, military combats,

election campaigns, industrial disputes and lawsuits where one-sided submission and

two-sided peace between the parties can occur as a Cournot equilibrium.

86


Appendix

Proof of proposition 1:

The first order condition equation states:

r\ = 1 > a > 0 (A .l)a X

Agents will expend positive effort only in the case when they can achieve positive

expected profits:

rV,*)>0 o { I j r + | j r A ( r 1, ) - | j r A ( r J) - c ^ } > 0 (A.2)

r2 <*"' [*('i’ ) + - ---- ^77'f] (A.3)a a X

G(c,a,X)=h~l [ h ( r ; ) + - - ^ - r ; ] (A.4)a a X


The equilibrium expected profit of agent 1 involved in persuasion is:

V'* =[\ X + ~ \ X h ^ ~ c i (A'5)

V * = ^ X - c r (A.6)

similarly agent 2’s equilibrium expected profit takes the following form:

K + j X K r ) - j X K r ) ] - c r (A.7)

V"2 X x - c r (A.8)

Equilibria can exist only if the equilibrium profits of both agents are positive or if

V* > 0 (A.9)

87


V*>0 (A. 10)

This is equivalent to the conditions that:

» Xr, < — (A.l 1)

2c

ri < ~ (A. 12)2 c


A Nash equilibrium with 2 agents under asymmetric cost functions and

asymmetric contestable rents is such that both agents invest different amounts of

effort r* in persuasion with

r; = 1 > a > 0 (A. 13)a X x

1 > a > 0 (A. 14)a X 2

and

r - = (*■)-' ( S i - ) r ; (A.15)c2X,

The equilibrium equation above characterizes the shape of all possible Nash

equilibria between players 1 and 2 and is determined by the magnitude of

. w r ' ( \ )Ar = --------- —— = (h') — ~) ■ From Hao and Zheng (1998), we know that the' 2 C 2 X <

a X 2

inverse of an increasing (decreasing) monotone function is also increasing

88


(decreasing) which implies that (/f )"'(•) is a decreasing function since /?"(.) < 0.

* *V C C V c c

This implies that -v > 1 for —- < —— and -V < 1 for — > ——.X, X 2 r2 X, X 2


See proof of proposition 3 above.



N rn = ( h Y ( — ), a >0 (A. 16)

a X

Agents will expend positive effort only in the case when they can achieve positive

expected profits:

7=1

V(r*)> 0 o - + — } - c r * } > 0 (A.17)lN N ' N N - 1, X a X , , a X ,\*j

r~-‘ < h-1 [h(r*)+— - — rf*] (A. 18)a a X

o G(N, c ,a , X) =h~l [h(r*) + - -----——r*] (A. 19)a a X


With N agents there can only be symmetric equilibria. This equilibrium can exist

only if the equilibrium profit is positive or if

Y ^ h i r )7=1

{ — ------------’N ' N ' v ' iV N - 1

This is equivalent to the condition that

V = [— + (— )/,(r * ) - ( — X— ------- )] -cr* > 0 • (A.20)

89


Xr < -----N c

(A.21)


If an interior Nash equilibrium in pure strategies exists, then the extent of rent

N c i _t N cdissipation is D = (-----)(h ) (-) . A necessary condition for the existence of anX ex, X

interior Nash equilibrium in pure strategies is (h ' y1 ( - ^ - ) < which implies thata X N c

the extent of rent dissipation is:

D < (— )(— ) (A.22)X N c

<=> Z) < 1 (A.23)

The change in D with respect to N can be shown by the representation below:

f = < > y < ^ ) + ( ^ ) { - ^ « A y ' ) ( ^ ) } (a .24,dN X a X X d N a X

From equation (A. 16) and from proposition 4 above, it can be easily shown that the

extent of rent dissipation D is increasing in the number of agents N when

>{h'Y1 > - N ((h ' y 1 ) ( - ^ r ) , and decreasing whenN c a X d N a X

t c c*0 <{h )_1 (----- ) < - N ------((h ) 1)(----- ). Similarly we can show that the extent of

a X d N a X

rent dissipation D is increasing in the cost per unit of persuasion activity c when

^ ->(h')~x ( ^ C) > - N — ((h ' y 1)(—— ), and decreasing whenN c a X dc a X

0 < ( h y ] ( - ^ - ) < - N —— ((h ) ' . It can be also shown that the extent of renta X dc a X

90


dissipation D is decreasing in the contestable rent X when

X „ 8 • j N c _->{h ) (----- )>X (\h ) )(----- ) , and increasing whenN c a X 8 X a X

a X 8 X a X



r* =( h ' y ' ( --------------------;-------- ), (A.25)W r - l ) J + [^ (E\,E2) + ( l -S - r )7r]Xh(r2)]

Agent 1 will expend positive effort only in the case when:

r* > 0 <=> n ( T - \ ) X + [7t\E\,E2) + ( \ - 8 - Y ) n } X h { r 2) > 0 (A.26)

, _ l r *(T -1 )<=> r2 <h ----------------------------- ]n (E\,E2) + ( l - S - T ) 7 r

(A.27)


With two agents there can only be asymmetric equilibria. This equilibrium can exist

only if the equilibrium profits are positive or if

V; = n X + p ± - 7 i { \ - 8 ) X h ( r ; ) - c r ; (A.28)h \rx )

and

v ; = (1 -7C)X + - 7t(T -1) X h(r; ) - cr2 (A.29)h \r2)

This is equivalent to the conditions that

j - l r C K r i ) Cr ,<h [------------1---------------------------------------- r21 (A.30)S r (T - l) n ( T - \ ) X h( r2) tt{T - \ ) X 2

and

91


1 h{r•*)1 - S 7 c ( \ - S ) X h (r[ ) - S ) X

•ir\ 1

92


(A.31)

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