SIGNALING GAMES AND

ACCOUNTABILITYMario Gilli

Department of Economics

University of Milano-Bicocca

• Introduction • In the past twenty years game theoretic models

have become a common paradigm in political economics.

• Political phenomena have been explained as a consequence of equilibrium behavior related to individual incentives inherent in a political system.

• Two are the crucial issues at the core of this literature: 1. To select congruent agent as rulers2. To find the correct mechanism to incentivize

congruent political behavior

• Signalling games have proved to be an effective means to model both issues, and their interaction.

• The aim of this paper is 1. to show the effectiveness of this approach

providing a general structure applied to different political issues related to the interaction between politicians' incentivation and selection

2. To show the crucial role played by the assumptions on the players’ beliefs to select different equilibria, i.e. different properties of political regimes.

• The main focus of the paper will be on the role of beliefs on the equilibrium properties of game theoretic models of accountability in political economics.

• The precise models analyzed in this paper vary widely, we select the models that have a common structure:

1. models that can be represented as signaling games

2. beliefs’ updating out of equilibrium is crucial,

• Signaling games are specific incomplete information games where the informed player moves first and in this way might convey information on its private information

The general structure of Signaling Games

• THE SIMPLEST POSSIBLE STRUCTURE• Two players: a Sender (S) and a Receiver (R).• The timing of the game is:

– (1) nature draws a type for S, denoted t  T, according to the commonly known probability distribution p(t);

– (2) S privately observes the type t and then sends the message m  M to R; and

– (3) R observes m and then takes the action a  A.• SIMPLIFICATION: T, M, and A are all finite.• Payoffs are US(t,m,a) and UR(t,m,a).• Everything but t, is common knowledge.

A possible game tree

Nature

1t

2t

Sender

Sender

receiver receiver

Sequential Rationality in Extensive Form Games

• After the Harsanyi transformation, signaling games are just a specific class of extensive form games with imperfect information.

• A well known problem of equilibrium behavior in extensive form games is that choices out of the equilibrium path are unrestricted by expected utility maximization, since they are conditioned to zero probability event.

• The fact is that in a Nash Equilibrium each player must act optimally given the other players' strategies

• However, this means that optimality condition is imposed at the beginning of the game only.

• Entry game as example.

The first equilibrium: Enter, Accomodate

1

0, 0

2, 2

1, 5

Enter

Smash

Stay Out

Accommodate

2

1z

2z

3z

The Entry Game

The second equilibrium: Stay Out-Smash

1

0, 0

2, 2

1, 5

Enter

Smash

Stay Out

Accommodate

1z

2z

3z

2

Meaning of the second equilibrium: Stay Out, Smash

• Threat by 2: if you will enter, I will smash you• But once 2 is called to play, will 2 have the incentive to

carry out the threat?– If YES, the action is credible– If NO, the action is noncredible

• In this equilibrium, if 2 will be asked to play, then 2 will prefer to accomodate: the threat is non credible

• How is it possible in a Nash equilibrium?• Nash Equilibrium: each player must act optimally given the

other players' strategies, i.e., play a best response to the others' strategies.

• Problem: Optimality condition only at the beginning of the game

Out of equilibrium information sets• In dynamic games there are equilibrium paths that do

not reach some information sets: these are the out-of-equilibrium information sets

• The optimality conditions of Nash equilibria does not constrain behavior at these nodes, but

• these information sets are out-of-equilibrium because of the actions the players are supposed to play at these nodes

• In other words, reaching these nodes in equilibrium is a zero probability event, but this probability is endogeneous, because is derived from the players’ equilibrium behavior.

Out of equilibrium information sets in the entry game

• Formally:

• Suppose 1 plays Stay out • Then player 2’s payoff does not depend on his

strategy

• Therefore any 2’s strategy is a best reply to 1’s SO

).(5)()(2)()(0

),|()(

),|()(),|()(

),(

12121

21332

2122221112

212

SOAESE

zPzv

zPzvzPzv

v

Sequential Rationality• An optimal strategy for a player should maximize his or

her payoff, conditional on every information set at which this player has the move• In other words, player i’s strategy should specify an “optimal” action at each of player i’s information sets, even those that have zero endogenous

probability to be reachedTHUS

• Apply some notion of rational behavior any time you face a well defined decision situation.

• This implies that players takes action that they do have an incentive (according to that notion of rational behavior) to carry out, once the information set is reached, even if it had ex ante zero probability.

The first equilibrium is the only one satisfying sequential rationality

1

0, 0

2, 2

1, 5

Enter

Smash

Stay Out

Accommodate

2

1z

2z

3z

The Entry Game

1

1

2

02

-3-1

1-2

-2-1

31

x x’

R

R

L M

l r l r

15

Sequential Rationality: a problem• An optimal strategy for a player

should maximize his or her payoff, conditional on every information set at which this player has the move

• However in some information sets, the optimal action depends1. On the other players’ future

behavior2. On the decision nodes of the

information set

• the optimal choice of 1 depends on 2 actions in {x, x’}

• In {x, x’} 2 would choose l if x, r if x’

• A behavior strategy for player i is the collection

where for each hHi and each aA(h), hi(a) 0 and

hi(a) is a probability distribution that describes i's behavior

at information set h. = (1,...,n) -i = (1,...,i-1,i+1,...,n).

i hi

h H(a)i

{ }

hi

a A(h)

(a) 1.

Construction of a formal definition of sequential rationality: notation

• A system of beliefssystem of beliefs is a specification h(x) for each information set h, where

• h(x) 0 is the probability player i assesses that a node x h Hi has been reached, GIVEN h Hi .

• Therefore

• An assessmentassessment is

a beliefs-strategies pair (,).

Hhxhx h

1)(

Construction of a formal definition of sequential rationality: definitions

Definition of SEQUENTIAL RATIONALITY

for imperfect information games

An assessment (,) is sequentially rational if given the beliefs

• no player i prefers at any information set h Hi to change her strategy h

i

• In other words,

• each player’s behavior strategy is a best response at any information set h

Hi, given her beliefs and -i

Effect of sequential rationality for imperfect information games

1. First, it eliminates strictly dominated actions from consideration off the equilibrium path: actions are credible

2. Second, it elevates beliefs to the importance of strategies.

• This provides a language — the language of beliefs — for discussing the merits of competing sequentially rational equilibria.

Definition of WEAK PERFECT BAYESIAN EQUILIBRIUM

A Weak Perfect Bayesian equilibriumWeak Perfect Bayesian equilibrium is an assessment (,) such that

1. each player’s behavior strategy is a best response at any information set h Hi, given her beliefs and given opponents’ equilibrium behavior, i.e.

for any hH, (h) BR(h, -i )

2. The beliefs are derived from the equilibrium strategies through Bayes’ rule whenever possible, i.e.

)( ));(Pr(

);Pr())(|(

0));(Pr( such that )(

xhxxh

xxhx

xhxh

THE PROBLEMS WITH WPBE AND THE NOTION

OF SEQUENTIAL EQUILIBRIA

Game 2: WPBE and beliefs

1

1

2

02

-3-1

1-2

-2-1

31

x x’

R

R

L M

l r l r

Problem: A WPBE might be supported by strange beliefs

Two WPBE:

1.(RM,r), with

2. (RM,l) with

1))(|( xhx

1))(|'( xhx

22

Game 2: deriving beliefs for a WPBE(R-M, l)

1

1

2

02

-3-1

1-2

-2-1

31

x x’

R

R

L M

l r l r

repliesbest are ,

then ,1))(|( Suppose

]1,0[))(|(

0

0

)()()()(

)()(

));(Pr(

);Pr())(|(

:R playing from ruleBayesian

through beliefs Deriving

1111

11

lM

xhx

xhx

MRLR

LR

xh

xxhx

Refining the notion of Weak Perfect Bayesian Equilibrium

• To solve the previous problem we try to refine the notion of WPBE, using totally mixed strategies and defining SEQUENTIAL EQUILIBRIA.

• A strategy profile is totally mixed

if it assigns strictly positive probability to each action a A(h) for each information set h H.

Definition ofSEQUENTIAL EQUILIBRIUM

• An assessment (,) is consistent if there exists a sequence of totally mixed strategies n and corresponding beliefs n derived from Bayes' rule such that

• A sequential equilibrium is an assessment (,) that is both

1. sequentially rational and

2. consistent.

limn

n n( , ) ( , ).

Game 2: deriving beliefs with consistency

1

1

2

02

-3-1

1-2

-2-1

31

x x’

R

R

L M

l r l r

1 1

1 1 1 1

0

Deriving consistent beliefs through

Bayesian rule from playing RM,l:

Pr( | )( | ( ))

Pr( ( ) | )

( ) ( )

( ) ( ) ( ) ( )

0(1 ) 1

( | ( )) 0

then , are NOT best re

xx h x

h x

R L

R L R M

x h x

M l

plies

the unique SE in pure strategies is

( , ) which is Subgame PerfectRM r

DIFFERENT REFINEMENTS AND DIFFERENT

EXPLANATIONS OF DEVIATIONS

27

Meaning of SEQUENTIAL EQUILIBRIA

• In a SE any equilibrium strategy is approximated by a totally mixed strategy

• Because of this, any information set is reached with strictly positive probability possibly vanishing

• This means that out of equilibrium information sets are reached with small vanishing probabilities, i.e. by mistakes:

impossible events are explained as due to trembling hands.

SIMPLE MISTAKES

• The simplest explanations of a deviation from the equilibrium path is just a simple mistake:– One holds to the hypothesis that all players intend to

follow the prescription of the equilibrium, but that they sometimes fail

• In Signaling Games useful restrictions on out-of-equilibrium beliefs are possible only insofar as one is willing to attribute relative likelihood to particular mistakes. 29

Sequential Equilibria in Signaling Games

n

p1

n

p2

n

p11

n

p21

x

y

1

1 2

11 2

21 2

1

2 12

( ) [0,1]

1

0

( ) 1 1

px

p p

p if p o pp

x if p pp

if p o pp

Therefore any out-of-equilibrium beliefs is

possible both with WPBE and with SE. The value of μ will depend on p¹

versus p², i.e. whether we

believe is more likely that t¹ or t² has

deviated from SE

MISTAKEN THEORIES (1)• Deviations from equilibrium play may be explained by

the fact that one or more players does not understand what is expected of him or wish to signal something

• One would then look for relatively likely alternative theories for how to play the game to explain

1. Who has defected

2. What has been the nature of defection

3. Why some player has deviated , e.g. what might be the consequences of that defection for later play.

Structural consistency is a way of formalizing this type of reasoning.

31

MISTAKEN THEORIES (2)• this reasoning can lead to direct attack to Sequential

Equilibrium, in particular to the hypothesis that• player countenance no further deviations from the

equilibrium when evaluating what to do in the face of an apparent deviation,

• for example if after a deviation one believes that the error in theory may be one’s own, then deviations among different players may be thought to be correlated.

• Forward Induction: a deviation might be due to a prospective attempt to get a better payoff, e.g. a deviation from a specified equilibrium is said to be "bad" if it always yields the deviator less than her equilibrium payoff in every circumstance, according to FI this deviation should generate beliefs equal to zero

32

1

2

11

2-1

-4-2

-1-2

0-1

x x’

R

L M

l r l r1

1 1

11

1 1

Deriving beliefs through

Bayesian rule from playing R:

Pr( | )

Pr( ( ) | )

( ) 0[0,1]

( ) ( ) 0

Suppose ( | ( )) 0, then

, are sequentially rational however

( )( | ( )) 0 ( )

( ) ( )C

x

h x

L

L M

x h x

R r

Lx h x L

L M

0

Example of an implausible WPBE

(A,r) seems unreasonable because it requires player 2 to believe with high probability that player 1 has made a bad deviation from the equilibrium: it is not a forward induction equilibrium Limitations: in more complex games the set of bad deviations often is empty

SIGNALING GAMES

EQUILIBRIA & BELIEFS

Types of equilibria• POOLING EQUILIBRIUM: An equilibrium

where all types of informed players do the same thing, thus no information is provided by informed actions

• SEPARATING EQUILIBRIUM: An equilibrium where all types of informed players do different thing, thus information is perfectly revealed by informed actions

• SEMISEPARATING EQUILIBRIUM: An equilibrium where some types of informed players do different thing, thus information is partially revealed by informed actions

Example of possible pooling equilibrium

Example of possible separating equilibrium

1t

2t

3t

Example of possible semiseparating equilibrium

Refinements in Signalling Games

Beer and Quiche: The Entry-Deterrence Problem

N

wimp

surly

0.1

0.9

quiche

quichebeer

beerduel

duel

duel

duel

not

notnot

not

1;2

3;1

0;0

2;1

0;2

1;0

2;1

3;1

x

y’x’

y

Beer and Quiche: Two Sequential Equilibria

• Two SE, both pooling:1. (BB; ND): both types drink beer, and the entrant

duels if quiche is observed but declines to duel if beer is observed. To find a WPBE we should derive the possible beliefs that makes such decisions sequentially rational

2. (QQ; DN): both types have quiche, the entrant duels if beer is observed but declines to duel if quiche is observed. To find a WPBE we should derive the possible beliefs that makes such decisions sequentially rational.

First Sequential Equilibrium

The first pooling SE (BB; ND) with beliefs:

Hence ND should satisfy

Then the SE is

(BB; ND), (x|{x,x’}) = 0.1, (y|{y,y’}) ≥ 0.5.

]1,0[:0

0

09.001.0

01.0

)|()()|()(

)|()(|',|

1.019.011.0

11.0

)|()()|()(

)|()(|',|

SQSWQW

WQWQWyyy

SBSWBW

WBWBWxxx

5.0for satisfied always

)1(11)1(02|}',({|}',({

satisfied always 9.001.029.011.01|}',({|}',({

22

22

yyNEuyyDEu

xxDEuxxNEu

First SE: beer-beer, then μ(x|{x.x’})=0.1& μ(y|{y,y’})[0,1]; μ(x|{x.x’})=0.1 implies not. In turn this implies that 1will not deviate if and only if

2 duel in {y,y’}, i.e. μ(y|{y.y’}) > 1/2

N

wimp

surly

0.1

0.9

quiche

quichebeer

beerduel

duel

duel

duel

not

notnot

not

1;2

3;1

0;0

2;1

0;2

1;0

2;1

3;1

x

y’x’

y

First Sequential Equilibria

• Both types drink beer, and the entrant duels if quiche is observed but declines to duel if beer is observed.

In such an equilibrium, the decision to duel following quiche is rationalized by any off-the-equilibrium-path belief that puts sufficiently high probability (at least 1/2) on the incumbent being wimpy given that the non equilibrium choice “quiche” has been observed:

μ(y|{y,y’}) = μ(W|Q) > 1/2

Second Sequential EquilibriumThe second pooling SE (QQ; DN):

Hence DN should satisfy

Then the SE is

(QQ; DN), (x|{x,x’}) ≥ 0.5, (y|{y,y’}) = 0.1

1.019.011.0

11.0

)|()()|()(

)|()(|',|

]1,0[:0

0

09.001.0

01.0

)|()()|()(

)|()(|',|

SQSWQW

WQWQWyyy

SBSWBW

WBWBWxxx

satisfied always 9.001.029.011.01|}',({|}',({

5.0for satisfied always

)1(11)1(02|}',({|}',({

22

22

yyDEuyyNEu

xxNEuxxDEu

Second SE: quiche-quiche, then μ(y|{y,y’})=0.1& μ(x|{x,x’})[0,1]; μ(y|

{y,y’})=0.1 implies not. In turn this implies that 1will not deviate if and only if 2 duel in {x,x’}, i.e. μ(x|{x,x’})>1/2

N

wimp

surly

0.1

0.9

quiche

quichebeer

beerduel

duel

duel

duel

not

notnot

not

1;2

3;1

0;0

2;1

0;2

1;0

2;1

3;1

x

y’x’

y

Second Sequential Equilibria

• Both types have quiche, and the entrant declines to duel if quiche is observed but duels if beer is observed.

• In such an equilibrium, the decision to duel following beer is rationalized by any off-the-equilibrium-path belief that puts sufficiently high probability (at least 1/2) on the incumbent being wimpy given that the non equilibrium choice “beer” has been observed:

μ(x|{x,x’}) = μ(W|B) > ½

• But here such beliefs seem unnatural: the prior belief is .9 that the incumbent is surly, but when conditioned on the observation of beer - which is preferred if surly but not if wimpy - the posterior belief is at least .5 that the incumbent is wimpy.

Sequential EquilibriaHow can we reject the second equilibrium?• Using the intuitive criterion one can argue that surly

will find it optimal to deviate from the proposed equilibrium:

• if S is type t’, the following speech should be believed by R:I am t'.

To prove this, I am sending m' instead of the equilibrium m. Note that if I were t I would not want to do this, no matter

what you might infer from m'. And, as t', I have an incentive to do this provided it convinces

you that I am not t. • If the entrant concludes that the beer-drinker is surly,

then declining to duel is the optimal decision. This yields a payoff of 3 for surly, which is better than the 2 earned in equilibrium.

SIGNALING GAMESEQUILIBRIA and BELIEFS

inPOLITICAL ECONOMICS

MODELS:THE ACCOUNTABILITY

PROBLEM

Accountability and Signalling Games

• Two models to understand the determinants of good government.

• The basic idea is that good government is associated with institutions which affects the incentives and the selection of those who make policy decisions.

• The incentive problem is studied analyzing the possible equilibria of principal-agent models between citizens and government, where the principals are the citizens and the agents are the politicians.

• The heart of these models is rulers' accountability towards citizens, i.e. the responsibility of rulers as agents towards the citizens and the political elites as principals

• Whether and how accountability is achieved depends on the rules of the game.

Accountability in Democratic

Polities

Accountability in Democratic Polities • In democracies, elections are the main tool to enforce

government accountability towards citizens. • We will consider a model that assume that voters do

have a common interest in achieving some outcome and discuss whether we would expect the political system to deliver it.

• Basic Model – Two-period political-agency model with incomplete

information played by two protagonists: the leader and the citizens.

– the leader is elected to make a single political decision. – The key issue is the use of this policy choices as a

signaling device as different type of politicians try to differentiate themselves from one another.

EXTENSIVE FORM - PLAYERS AND PAYOFFS:1. Two players, the leader (L) (female) and the voters (V)

(plural).2. In each period t=1,2 the leader is elected to make a single

political decision, denoted by et {0,1}. ∈3. The payoff to voters and leader depend on the true state of

nature θt {0,1} which is only observed by the incumbent ∈leader, – Voters and leader receive a public payoff of Δ if et = θt and zero

otherwise. – The leader can be one of two types, either congruent or non-

congruent, T {C, N}, with probability π of being congruent. ∈All leader get a payoff E from holding office

– The congruent leader share voters' objectives exactly. – The non-congruent leader receives a private benefit rt [0,R] ∈

from picking et ≠ θt, where rt is drawn according to a continuous cumulative distribution function G(rt) with G(Δ)=0, G(rt)>0 for rt>Δ, and R>E(r)+E; whereas the congruent leader obtains no private benefit from selecting et ≠θt.

EXTENSIVE FORM – TIMING:1. Nature determines (θ₁,r₁) and the type of the leader T {C,N} ∈

and their realization is private information of the dictator.2. Type T leader chooses a policy, and the payoffs for each player

in period one are realized. – The probability of choosing a period 1 efficient policy e₁=θ₁ is

denoted by λ₁T: r₁ [0,1]↦3. The voters observes the realization of their payoff δ {0,Δ}, on ∈

the basis of this information decides whether to re-elect the incumbent leader. – The probability of re-electing the leader is denoted by ρ:δ [0,1]↦

4. If the incumbent leader is ousted from power, a new leader will enter office and she will be congruent with a probability of π. Otherwise the incumbent leader is still in power.

5. The game enters the second period and nature determines (θ₂,r₂).

6. Type T leader chooses a policy, and the payoffs for each player in period two are realized. – The probability of choosing a period 2 efficient policy e₂=θ₂ is

denoted by λ₂ T: r₂ [0,1].↦

C LEADER

=

=

CITIZEN

=0

=0

NC LEADER

CITIZEN

Oust

Oust

Oust

Oust

Not Oust Not Oust

Not Oust

Bad policy

Bad policy

Good policy

Good policyNot Oust

FIRST STAGE GAME

PERFECT BAYESIAN EQUILIBRIA

1. Sequential rationality implies that after δ {0,Δ} ∈ the voters will re-elect the incumbent leader if and only if:

• As usual, μ(C|δ) is derived using Bayes rule:

1 1 0

| 1 | 0 1 0

1 |

0 |

v vV V

C C

C

C

1 1 1

1 1 1 1 1 1

1 1 1

1 1 1 1 1 1

,

, 1 ,|

1 ,0

1 , 1 1 ,

C

C N

C

C N

r

r rC

r

r r

Perfect Bayesian Equilibria• Examine all the four possible

incumbent's strategy profiles. • To solve beliefs' indeterminacy out-

of-the equilibrium path use forward induction: any deviation towards efficiency is due to the C type, otherwise is due to the N type.

C LEADER

=

=

CITIZEN

=0

=0

N LEADER

CITIZEN

Oust

Oust

Oust

Oust

Not Oust Not Oust

Not Oust

Bad policy

Bad policy

Good policy

Good policyNot Oust

Perfect Bayesian Equilibria – 1

1.λ₁C = λ₁N = 0

010,1

| 00

0

1

0,1 0

because of F.I.C

then type C would deviate, it is not a SE

C LEADER

=

=

CITIZEN

=0

=0

N LEADER

CITIZEN

Oust

Oust

Oust

Oust

Not Oust Not Oust

Not Oust

Bad policy

Bad policy

Good policy

Good policyNot Oust

Perfect Bayesian Equilibria – 2

1.λ₁C =0, λ₁N = 1

then type N would deviate, it is not a SE

0 0|

1 0 1 0C

C LEADER

=

=

CITIZEN

=0

=0

N LEADER

CITIZEN

Oust

Oust

Oust

Oust

Not Oust Not Oust

Not Oust

Bad policy

Bad policy

Good policy

Good policyNot Oust

Perfect Bayesian Equilibria – 3

1.λ₁C =1 λ₁N = 0 1 1|

0 0 0 0C

then type N would not deviate iff

1 1 i.e. with prob. 1r E E E r E r E r E G E r E

1 1Hence |

0 0 0 0 00

0 1 1

GC

G

C LEADER

=

=

CITIZEN

=0

=0

N LEADER

CITIZEN

Oust

Oust

Oust

Oust

Not Oust Not Oust

Not Oust

Bad policy

Bad policy

Good policy

Good policyNot Oust

Perfect Bayesian Equilibria – 4

1.λ₁C =1 λ₁N = 1

Suppose ()=1,

1 1 i.e. with prob. r E E E r E r E r E G E r E

1 1Hence |

0 0 0 0 00

0 1 1

GC

G

0,1| because of F.I.=0

0 00,1 0 0 00

C

then type N would not deviate iff

CONCLUSION

• we can conclude with the following proposition

• The accountability game for democratic regimes has a unique FORWARD INDUCTION PBE where

• NB: 1. the probability of an efficient policy is increasing in , R(r)

and E

2. In equilibrium there is leader turnover iff policy is inefficient

1 1 1 1 1 1

2 2 2 2 2 2

, 1, , ,

, 1, , 0

11 with |

0 00 0

C N

C N

r r G E r E

r r

GC

Perfect Bayesian Equilibria with

PASSIVE UPDATING• Examine all the four possible

incumbent's strategy profiles. • To solve beliefs' indeterminacy out-

of-the equilibrium path use passive updating: any deviation is due to both types, with equal probability

C LEADER

=

=

CITIZEN

=0

=0

N LEADER

CITIZEN

Oust

Oust

Oust

Oust

Not Oust Not Oust

Not Oust

Bad policy

Bad policy

Good policy

Good policyNot Oust

Perfect Bayesian Equilibria – 1

1.λ₁C = λ₁N = 0

** *

**

00,10,1

| because of P.U.=00,1 00

0

0,1. . , then it is a SE iff 0

0,1 0

C

i eE

C LEADER

=

=

CITIZEN

=0

=0

N LEADER

CITIZEN

Oust

Oust

Oust

Oust

Not Oust Not Oust

Not Oust

Bad policy

Bad policy

Good policy

Good policyNot Oust

Perfect Bayesian Equilibria – 2

1.λ₁C =0, λ₁N = 1

then type N would deviate, it is not a SE

0 0|

1 0 1 0C

C LEADER

=

=

CITIZEN

=0

=0

N LEADER

CITIZEN

Oust

Oust

Oust

Oust

Not Oust Not Oust

Not Oust

Bad policy

Bad policy

Good policy

Good policyNot Oust

Perfect Bayesian Equilibria – 3

1.λ₁C =1 λ₁N = 0 1 1|

0 0 0 0C

then type N would not deviate iff

1 1 i.e. with prob. 1r E E E r E r E r E G E r E

1 1Hence |

0 0 0 0 00

0 1 1

GC

G

C LEADER

=

=

CITIZEN

=0

=0

N LEADER

CITIZEN

Oust

Oust

Oust

Oust

Not Oust Not Oust

Not Oust

Bad policy

Bad policy

Good policy

Good policyNot Oust

Perfect Bayesian Equilibria – 4

1.λ₁C =1 λ₁N = 1

*

*

0,1| 0

0 0 0,1 00,1 00

C

Type C of the leader would not deviate iff * * 0 - E

Type N of the leader would not deviate with prob * * 0 0 * * 0G E r E

1 1Hence |

0 0 0 0 00

0 1 1

GC

G

CONCLUSION• we can conclude with the following proposition• The accountability game for democratic regimes has

multiple PBE with passive updating:

1 1 1 1 1 1

2 2 2 2 2 2

1 1 1 1 1 1 2 2 2 2 2 2

*

*

1. , 1, , ,

, 1, , 0

11 with |

0 00 0

2. , 0, , 0, , 1, , 0

0,1

0 0,1

C N

C N

C N C N

r r G E r E

r r

GC

r r r r

* * with 0 - 0

and |0

E

C

• NB: In the second equilibrium there is

1. Inefficient policy with probability one, even if the leader is congruent

2. Voters believe that all leaders are the same, hence they choose randomly

Hence it might be interpreted as a “populist equilibrium”.

Accountability in Autocratic Polities

Accountability in Autocratic Polities • The purpose of this part of the paper is to explore

autocratic decision making when policy choices are constrained by the joint work of two mechanisms: 1. the threat of a coup d'état by the political elite and 2. the threat of a revolution by the citizens.

• How will the actual policy choices be affected by the political institutions and in particular by these players' de facto power?

• Our analysis will help to explain when and why the policy choices are congruent and in this way it will provide a partial understanding of the evidence that autocracies have both the strongest and the most negative growth rates across and within countries.

The model• A two-period political-agency model with

incomplete information played by three protagonists: 1. the dictator,

2. the selectorate, and

3. the citizens.

• Contrary to standard political-agency models for democracies, there is no regular general election, hence the dictators' term might be indeterminate.

• However, dictators can be removed from office by 1. the selectorate through a coup or

2. by the citizens through a revolution.

The model• Dictators differ in their ability to control the selectorate

and repress the citizens.

• To model this institutional difference, we introduce two separate conflict technologies, one for coups and one for revolutions. 1. Revolutions are defined as popular revolts whose goal is a

permanent change in the distribution of a country's wealth.

2. Coups, instead, are defined as a forced resignation of the dictator without any transformation in the political regime. A coup does not change the distribution of a country's wealth instead changes the composition of the selectorate and the identity of the dictator.

• Hence, the threat of a revolution is different from the threat of a coup.

=

=

=0

=0

C LEADER

NC LEADER

Bad policy Good policy

Bad policy Good policy

SELECTORATE SELECTORATECITIZEN CITIZEN

Oust

Oust

Oust

Oust

Not Oust Not Oust

Not OustNot Oust

Revolt

Revolt

Revolt

Revolt

Revolt

Revolt

Revolt

Revolt

Not Revolt

Not Revolt

Not Revolt

Not RevoltNot Revolt

Not Revolt

Not Revolt

Not Revolt

1

X

X X

X

X Failed State

Partially or Efficient Autocracies

Predatory AutocraciesSmall prob of

efficientpolicies, revolts

and//or coups

Positive prob of efficientpolicies

no revoltspossible coups

Small prob of efficientpolicies

no revolts and no coups

THANKS !