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A Thesis on Sabotage in Competitions

by

Oliver Alexander Wray

Trinity College

University of Dublin

on exchange at

University of Cologne

Under Supervision of Prof. Dr. Oliver Gürtler

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CONTENTS

1 Title Page

2 Table of Contents

3-14 Thesis

3 Introduction and Aim of Thesis

4-11 Elucidation of Paper

4-6 I. The Competitive Structure

7-8 II. Personality Counts

9 III. Multiworker Firms

10-11 IV. Other Issues

12-14 Critique

15 Conclusion

16 References

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INTRODUCTION AND AIM OF THESIS

In his 1989 paper ‘Equality and Industrial Politics’ Edward Lazear examines the rationales

behind, and result of, both management and union desires for workers to receive equal wage

treatment. Given the axioms of natural variation in productivity between workers in a firm, and

that under no wage adjustment more productive workers would be paid more having produced

more and won the ‘tournament’, Lazear concedes early in his paper that ‘[T]he morale of high-

quality workers is likely to be adversely affected by pay that regresses towards the mean’ and

that the morale increase of the rest of the firm’s workers does not necessarily improve to the

extent that it offsets the initial morale impairment. He does not attempt to salvage this negative

attribute resulting from equal wage treatment. Yet he overshadows this by positing in the

introduction that this wage ‘compression’ derives from ‘an attempt to preserve worker unity,

to maintain good morale, and to create a good work environment’. Lazear ultimately concludes

in agreement with this latter qualitative hypothesis, albeit in the terms of efficiency; ‘if

harmony is important, pay compression is optimal on strict efficiency grounds’. The intuit ion

behind this thought process is that if the wage spread is reduced for different levels of worker

output, then workers will be less inclined to sabotage other, usually more productive workers,

thereby reducing the average production in the firm, and thereby increasing their pay when

based off of the average (referred by Lazear as the ‘reference’). Of course, any sabotage at all

reduces the firm’s potential output, and would want to be avoided wherever possible by

management. This is also deduced from the result of mathematical expansions of equations for

workers’ activity bundles, – a function of productive effort and sabotage of other workers’

production – optimal solutions to workers’ problems in various situations, the firms’ problem,

pay equality and other formulae. As a result of these mathematical arguments which agree with

the theory that at least some pay compression is efficient, he also discerns that firms rationally

take personality (split into ‘hawks’ and ‘doves’, whereby the marginal cost of sabotaging a co-

worker’s work is higher for doves than for hawks) into account when hiring new workers. A

third and final conclusion unearthed is that of hierarchy’s impact on worker composition and

the resulting wage compression. As these jobs tend to be filled by more hawkish, competit ive

individuals than other areas of the same firm, pay may be closer to a piece rate system whereby

there is no relationship between pay and the group’s average pay, or even based on the

performance of the firm as a whole, thereby eliminating any incentive to sabotage another’s

work.

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The aim of this thesis is to expand on the above summary of the four main chapters of

Lazear’s 1989 paper in a piecemeal fashion. This will include contemporary examples

illustrating Lazear’s arguments and critique of some areas of his thoughts and theoretica l

reasoning. A general critique of the paper as a whole will follow, including Henk Thierry’s

Reflection Theory on pay having no significance in itself psychologically, but it acquiring

meaning to the extent that it conveys information that is important to the worker’s self-identity,

which in turn influences the action bundle of an employee. Satisficing, and its relationship to

a change in pay will also be examined in the main body of the thesis. The main critique of the

paper however will be that of the omission of the role of time, which will be explored in depth.

Finally, the paper will conclude and summarise.

ELUCIDATION OF PAPER

I. The Competitive Structure

The initial basic model used by Lazear is one of two players representing employees in a firm,

j and k, with output qj and qk. The firm’s output is Q = Q (qj, qk), where:

qj = f (μj, θk) + εj and qk = f (μk, θj) + εk

μj and μk are defined as effort by j and k respectively. θk and θj is k’s sabotage (in a practical

sense, not giving other workers information that would make them more productive) on j and

j’s sabotage on k respectively.1 εj and εk are random terms arising from productive luck or

measurement error, such that E(ε) is zero. When introducing costs for workers’ action bundles,

we need to split workers into the types described in the introduction – hawks and doves. Their

respective cost functions are: CH (μ, θ) and CD (μ, θ)2. Given everything in a tournament is

relative, what is important for us is the difference between what the winner in the production

competition receives (w1) and the loser (w2). In such a tournament with two identical hawks

competing, hawk j wants to maximise the following problem including costs:

WORKER MAX: W1 P (μj, θj; μk, θk) + W2

[1 – P] - CH (μj, θj)

Where P (μj, θj; μk, θk) is the probability that j wins the tournament, conditional on his choice

of μ and θ in his or her activity bundle. It is noteworthy here that given both hawks are identica l,

1 Unless stated otherwise, for this thesis it will always be assumed that sabotage is always possible 2 As stated in the introduction, the marginal cost of sabotage is greater for the doves than the hawk:

δCH (μ0, θ0) < δCD (μ0, θ0) for every μ0 and θ0.

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the optimal solution to the above equation will be identical levels of μ and θ for both workers.

These respective optimals are the first order conditions set equal to zero, or, graphically, the

highest stationary point on a graph with μ or θ on the X axis and P on the Y axis, with the

relationship itself being akin to that of a marginal product of labour line, initially increasing P

with μ or θ, before declining after the maximum stationary point. The respective first order

conditions for player j are:

(W1 -W2) δP/δμj = (W1 -W2) g [f (μj, θk) – f (μk, θj)] = C1H (μj, θj) = C1

H (μj, θj)/f1 (μj, θk)

(W1 -W2) δP/δθj = (W1 -W2) g [f (μj, θk) – f (μk, θj)] = C2H (μj, θj) = -C2

H (μj, θj)/f2 (μk, θj)

And for k, whose values will be identical given j and k are identical, hence the simplification:

(W1 -W2) δP/δμk = (W1 -W2) g [0] = C1H (μk, θk) = C1

H (μk, θk)/f1 (μk, θj)

(W1 -W2) δP/δθk = (W1 -W2) g [0] = C2H (μk, θk) = -C2

H (μk, θk)/f2 (μj, θk)

Where g is the distribution function of the error terms εk - εj.

The second and fourth equations (first order conditions for sabotage for j and k) show that

increasing the wage spread – the far left hand figure – must yield an increase in the level of

sabotage, θ, in order to keep the equation balanced. Conversely, an increase in wage equality

results in less sabotage. This is in accordance with Lazear’s initial hypothesis. However,

extending this argument to the first and third equations of the first order conditions with respect

to effort, μ, pay equality also reduces the amount of effort per worker. But in order to prove

that management too wants equal pay structures, instead of deducing it through intuition that

it increases both net output per worker and net total output, let us examine the firm’s problem:

FIRM MAX3: E {Q [f (μj, θk) + εj; f (μk, θj) + εk] – C (μj, θj) - C (μk, θk)}

As described earlier, it is clear that workers’ levels of μ and θ depend only on the wage spread.

So W1 - W2 = Δ where Δ stands for ‘change in’ our factors of μ and θ. Yet the level of W1 - W2

are both fixed by the zero profit condition! Thus the firm’s problem is now:

MAX: E {Q [f (μj(Δ), θk(Δ)) + εj; f (μk(Δ), θj(Δ)) + εk] – C (μj(Δ), θj(Δ)) - C (μk(Δ), θk(Δ))}

As above with the worker, the optimal solution fis the first order condition (with respect to μ):

E [Q1 (f1 μ’ + f2 θ’) – C1 μ’ – C2 θ’) = 0 (as Q is symmetric as the players are identical).

3 Subject to a zero expected profit condition, whereby: W 1 + W2 = E [Q (qj, qk)]

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Isolating C1 on the right hand side, implies C1 = E [(Q1f1 + (Q1f2θ’)/μ’ – (C2θ’)/μ’].

It is clear both mathematically and intuitively that effort is lower when at least some sabotage

does exist (C1 increases with increasing μ). It follows therefore that net output is lower when

sabotage exists, as sabotage ‘replaces’ some effort in the worker’s action bundle. However,

one must recall from the worker’s optimisation equation that pay equality also reduces each

worker’s effort. Nevertheless, the firm still looks to reduce the level of sabotage by way of

reducing the wage spread between the winner and loser in a competition, in the hope of seeing

lower sabotage, which results in higher average and total output.

So, to recap, hawks ‘attack’ each other in pursuit of the higher award for winning the

output competition, so firms select more equal wages for hawks to reduce their sabotage of one

another, however, the trade-off of this is that it also reduces their effort, μ. Empirically too, this

idea holds water. In traineeship programmes at the European Central Bank for example – a

rigorous employment opportunity where one would expect Europe’s most driven, competit ive

individuals to be working – all employees are paid a flat rate of €1900 per month, regardless

of performance (Europa, 2014). Yet on the other hand, even though sabotage has always been

assumed possible, there is nothing that constrains sabotage to be greater than zero for a worker.

Indeed, for very dovish workers with a very low cost function (what Lazear calls ‘a saint’) in

a setup where the wage spread is nevertheless low, a worker may be willing to perform anti-

sabotage (increase the other’s work output) despite it increasing his chances of losing the

competition and receiving the lower pay W2, due to the ‘utility of fellowship’ the worker

derives from doing so. This is shown below, where the optimal level of sabotage is the first

order condition of the worker’s problem with respect to θ, having already derived μ*:

(Lazear, 1989,

p.569)

However, when Lazear posits that ‘increasing the wage differential’ by way of a shift of the

optimum further up the Y axis on the above graph to increase optimal level of sabotage, which,

as he puts it, ‘tempts even the saint’, he is correct only in so far as he follows his theory that

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the value of the first order condition with respect to sabotage being linear. Given that the saint

is happy to accept W2 as he is better off losing the competition but deriving ‘utility of

fellowship’, it seems possible that he has reached his satisficing level of income at W2. If the

change in the wage spread was not great, especially if it were a result of a proportionally larger

increase in W1 than decrease in W2 (of which he would only care about the latter), then it seems

improbable that the saint would consider using sabotage or even attempt to win the competition

at all until the wage spread became very large and he was no longer at his satisficing level of

income. This would manifest as a more quadratic function of the derivative, with negative θ

values for most values of the wage spread, until the spread became excessively at which point

he would only then lose his ‘saintly’ status. Of course, if the derivative function in question

here is not linear as depicted, then the worker’s problem for saints may be different too.

II. Personality Counts

Lazear then considers the firm’s actions in matching up the two types of workers or keeping

them separate. Firms should, of course, segregate hawks from doves – hawks prefer to work

with doves as it is easier for them to win the competition as they are prepared to use sabotage

and the wage spread will be higher, yet workers do not necessarily self-sort when applying for

jobs in firms. Indeed by contrast, instead of looking for a firm of other hawks, it would be

advantageous for a hawk to work in a firm full of doves when possible. Consider the fact that

in a firm of only one type of worker, the average hawks’ output (q*H) in the hawkish firm is

lower than doves’ (q*D) in the dovish firm, as hawks devote more of their action bundle to

sabotaging each other. If we combine both this and the zero profit condition, then in a two

worker framework, it is clear that ((W1 + W2)/2) D > ((W1 + W2)/2) H. Thus, both hawks and

doves will prefer to work with doves. Therefore, the dovish firm with the relatively high W1

should certainly scrutinise the personality of all incoming workers to ensure that all are doves,

as there is certainly an incentive for a hawk to imitate being a dove to be hired by the firm.

Hawkish firms however should not have this concern. Given no doves would try to work there

as they would both receive more pay at both W1 and W2 and win more competitions at dovish

firms, the best course of action for the dovish firms may be to try and convince potential

applicants of their dovishness. This certainly seems the case empirically; the doubtless hawkish

firm of Goldman Sachs claims on its website to be ‘built on… collaboration, teamwork and

integrity’ (Goldman Sachs, 2014).

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Lazear outlines a theoretically possible alternative to firms being 100% either hawkish

or dovish that exists – that of personality contingent wages. If firms could in fact perfectly

distinguish between hawks and doves, then they could optimally run a firm with both present,

via utilising contingent wages. Here, winning (and losing) prizes are contingent on personality,

in such that a victorious hawk earns a lower W1 than a victorious dove. If both wages for both

sets of workers are set correctly, any μ* and θ* allocation that was available through the pairing

of the same type of workers isolated by firm is also achievable here. In both cases, the first

order conditions that the workers face are4:

(WD1 - WD

2) g (0) = CD1

(WD1 - WD

2) g (0) = CD2

(WH1 – WH

2) g (0) = CH1

(WH1 – WH

2) g (0) = CH2

However, real world problems not only of implementing such workplace ‘labelling’ but also

unequal pay by worker label result in this theory being confined to abstract practice. Thus, the

worker-type segregation by firm continues unimproved upon.

An alternative solution to the problem of mixed segregated firms is that of handicapping

workers. Returning to an employee’s action bundle (comprising entirely of either effort or

sabotage) and the assumption that workers can be correctly identified as either hawks or doves,

let us give the high cost worker type (here, doves - recall CH (μ, θ) < CD (μ, θ)) a handicap

equal to half the difference between the optimal effort for both types. Essentially, what this

results in is each type of worker’s cost function meeting the other in the middle. This results in

efficient effort choices for workers now their cost functions have similar forms, given that

workers choose the most efficient method of production given their cost function. This is

essentially the workers meeting their first order conditions back where they originally solved

the worker’s problem. Thus, such a handicap system achieves the same levels of μ and θ in an

integrated environment as that which would be achieved by segregation, and the levels of W1

and W2 are the same for all workers. However, the spreads used are still larger than what would

be expected in a dove only firm, and moreover the handicap does not blend the workers into a

4 This latter point is due to g(x) attaining its maximum at zero. Note here that g is again the distribution function of the error terms, εk - εj.

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single group. As with the earlier scenario of simply a firm hiring a mixture of doves and hawks,

dove workers will still see their chances of winning reduced from the 0.5 they saw in dove-

only firm scenarios, and hawks see their chances increase from the 0.5 they saw when they

worked in hawk only firms.

III. Multiworker Firms

Of course, few firms operate with the two workers we have modelled so far. Fortunately, the

results derived from a situation with two workers translate across perfectly into scenarios (that

is to say, firms) with more than two. For the sake of simplicity and to prove this point, let us

take a firm with three identical workers, eliminating the need for the hawk/dove distinction –

j, k and l. Again for simplicities’ sake, let us model sabotage as, what Lazear calls, a ‘public

bad’. By this, any choice of θ by one player adversely effects the output of both other players.

Therefore, the modified production function of all three workers takes this into account5:

qj = f(μj, θk, θl) + εj ; qk = f(μk, θj, θl) + εk ; ql = f(μl, θj, θk) + εl

(Where f2, f3 are less than zero, and f1 is greater than zero)

This is of course strikingly similar to the two worker firm example at the start of the paper. The

worker’s problem, also similar, likewise needs adjustment by way of introducing a third prize,

W3. Let P1 be the probability of winning, P3 for losing, and (1 – P1 – P3) for finishing second:

WORKER: MAX P1, W1 + (W2 (1 – P1 – P3)) + P3W3 – C (μj, θj)

The first order conditions with respect to effort and sabotage are respectively:

W1 (δP1/δμj) – W2 (δP1/δμj) – W2 (δP3/δμj) + /δμj) – C1 (μj, θj) = 0

W1 (δP1/δθj) – W2 (δP1/δθj) – W2 (δP3/δθj) + W3 (δP3/δθj) – C1 (μj, θj) = 0

This can be simplified greatly if we posit that j wins the game, setting P1 as:

P1 = Prob. [f (μj, θj) – f (μk, θk) > εk – εj and f (μj, θj) – f (μl, θl) > εl – εj]

And then that P3 as the reverse scenario, whereby j loses, l wins and k is second:

5 With regard to the error terms, assume equal density such that εj – εl ~ g (εj – εl), εj - εk ~ g (εj - εk) and εk – εl ~

g (εk - εl)

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P3 = Prob. [f (μk, θk) – f (μj, θj) > εj – εk and f (μl, θl) – f (μk, θk) > εj – εl]

Given that the density of εc – εd is identical and symmetric around zero, no matter what one

chooses for c or d, at the point of symmetric equilibrium, the error terms functions equal zero.

So, isolating for any worker i: δP1 / δμi = - δP3 / δμi and δP1 / δθi = - δP3 / δθi for all i.

Thus, the first order conditions for worker j can be written as:

(W1 – W3) δP1 / δμj = C1 (μj, θj) and (W1 – W3) δP1 / δθj = C2 (μj, θj)

What we have boiled down to is that with exception of replacing the losing wage of W2 with

W3 given there are now three prizes, for the first order conditions too, we have replicated the

results of the two player game. The firm’s problem too is identical, so all else holds equal.

Thus, the model of two workers is a fair one when used to describe phenomena in whole firms.

IV. Other Issues

If a worker finds it easy to (has a low marginal product of) sabotage, then perhaps he finds it

equally easy to put that action into effort (μ). Empirically this seems clear.6 One implication of

this is a revision of the statement earlier that hawks would attempt to pass themselves off as

doves as a result of pay being higher (and victories more frequent) in a purely dovish firm. In

our adjustment, some doves feign being a hawk to get hired in a high output, high pay hawkish

firm. Empirically too it is apparent that, as Lazear speculates ‘applicants are sometimes

aggressive in interviews’. Without delving into the realm of economic psychology at this stage,

whether or not such activities are a manifestation of attempting to convince an interviewer of

their low costs of effort is debatable, but they appear prevalent (Goldman, 2013).

But let us leave this notion aside and return to hawks and doves having lower marginal costs

of sabotage and effort respectively. Even if a hawk would try to hide his identity as a hawk

from management, frequent victories in competitions means management should note that they

are likely dealing with such a low cost worker. Yet the worker either is indeed a hawk and is

efficient at producing sabotage, or is simply a hard working dove who is efficient at producing

6 Although not explored in this thesis, this is in tune with Lazear’s claim that higher levels in the hierarchy of

the firm are filled with hawkish workers. Whilst these hawks by definition have a lower cost of sabotage than

the average worker, it seems unfeasible they reached that level in the firm relying purely on sabotage.

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effort. Consequently, some of the workers noticed by management to be frequently winning

are likely to be good saboteurs.

To demonstrate this, let us consider action as a whole, σ, that can be used as effort or sabotage7.

Let α be the proportion of all workers efficient at producing action. Regardless of whether or

not these workers are hawks or not in that they additionally have low cost of sabotage, let us

name these workers QUICKS. All other workers not QUICKS are SLOWS; i.e. equal to (1 –

α). Formally, this is written as CQUICK (σ) < CSLOW (σ) for any and all levels of action. Putting

in values for QUICK as A, and that the worker in question wins in a tournament as B in Bayes’

theorem8 notation, and defining the probability that the QUICK would win in a contest between

him and a SLOW as G* (it follows intuitively that G* > 0.5 as the QUICK would win more

often than the SLOW given his being more efficient at producing action). Thus:

Prob. (Quick | win) = α [2(1 – α) G* + α]

When making use of the fact that G* is greater than 0.5, we can simplify the above to:

Prob. (Quick | win) > α

Or, that a higher proportion of all competitions are won by QUICKS than the proportion of

QUICKS in the population. Given that the firm would intuitively promote those who win

frequently at competitions to higher levels in the firm’s hierarchy, the firm would unavoidab ly

promote numerous hawks, even more so than workers who produce effort efficiently that the

firm naturally wants higher up the management structure.9 Thus, the problem of sabotage in

competitions may be carried further up the firm from the hiring and production level discussed

earlier into the highest levels of management where hawks themselves direct other workers.

There are two solutions to this final issue. First, management level bonuses may be based on

the output of the firm as a whole rather than in relation to other senior level employees. This

would localise the problem of the hawks back down to the ‘entry level’ stage where it is still

unclear which workers are comparatively hawkish or dovish, whilst eliminating incentives for

any sabotage by management. But an alternative pan-firm solution is to, as Lazear puts it,

‘[keep] arm’s length relations between opposing contestants’. If two workers are to be put into

7 This thesis assigns ‘action’ and ‘effort’ to what Lazear calls ‘effort’ and ‘generalised effort’. The latter,

assigned the shorthand σ, is later itself referred to as ‘effort’ from page 576 onwards. The distinction in this

thesis is to avoid confusion between worker who have low costs of σ and μ – ‘sabotage’ and ‘effort’ respectively 8 Defined as Prob. (A | B) = (Prob. (B | A)*(Prob. A))/Prob. B 9 Recall that workers who are less efficient are producing sabotage are likely to lose in a competition with a

hawk, assuming that they are equally efficient at producing effort.

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a competition with each other, then distance should be kept between the two workers so that

one cannot influence the other. An example of this would be either selecting workers from

different branches of the same firm, or workers who have different tasks so that achieving the

definition of sabotage (see page 4) would be difficult without being blatant enough to warrant

investigation by a manager. But here too, the answer is not perfect; if a firm is divided up into

isolated branches that all have some obligatory functions such as filing tax reports, then keeping

workers and divisions isolated from each other results in inefficiencies from double-jobbing.

Lazear effectively makes both of these points by highlighting empirical ‘grouping by products’,

with the competitors for head of General Motors being selected from among the heads of one

of its ten separate brands, and lack of cooperation between the firms’ accountants respectively.

CRITIQUE

The first critique of Lazear’s paper is its lack of dynamism, or its assumption of no change in

the behaviour of workers across time. Assume that two identical workers were in a competition

with each other during a previous competition, and during the previous contest one worker

used at least some sabotage while the other allocated all his ‘action’ purely to effort. Let us

also assume perfect information about action bundles used by the other player, and that each

player is aware that they have faced their opponent before. Given diminishing marginal returns

to effort (and sabotage) the worker that chose to utilise more sabotage in the previous

competition is likely to have won. In his 1984 paper ‘The Evolution of Cooperation’, Robert

Axelrod conducted just such a tournament, and discerned that if played repeatedly, the most

successful strategy was a simple one he named ‘tit-for-tat’ (Axelrod, 2006). This involved

players cooperating in the first round, and then simply doing what the other player did

previously back to the same player in the next round. Applied in Lazear’s framework, the next

time two such workers are paired off in a competition again, it seems logical that the worker

who lost in the previous competition will ‘return the favour’ and modify his action bundle to

include more sabotage in the later round. This will not only be a result of the previously losing

worker looking to win this time in pursuit of W1; it will also include elements of wanting to

‘punish’ the other worker for sabotaging his output in the previous round.

In keeping with this idea of worker psychology influencing the outcomes of (and actions

within) tournaments is Henk Thierry’s Reflection Theory. First, let us deduce that one of the

purposes of the wage spread is to encourage workers to produce more output to win the

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competition, thus by extension producing more output for the firm. But Thierry posits that

while pay ‘reflects’ information about other fields, it has no significance in itself (Thierry,

1992). Instead, it ‘acquires meaning to the extent it conveys information that is important to

the employee’s self-identity’. Indeed, pay systems encourage such desired outcomes when the

pay’s meaning is stronger, rather than the wage spread on which Lazear focuses his paper. As

a prerequisite to the entirety of his paper, pay must first be made meaningful before it has any

effect on employees at all. The four methods that can help pay be made meaningful are

motivational properties, relative position, control and spending (Hakonen, 2014). The first of

these suggests that pay can be meaningful to an employee if a person considers the pay as a

medium of achieving important goals. Consider for instance a part-time job for a student over

a summer vacation versus a job for an employee close to retirement with a large allocation of

their income going into a pension programme. Both workers are originally paid hourly. If both

workers then entered into separate pay-by-performance tournament such as those outlined by

Lazear, it is likely that the effects would be more pronounced for the latter than the former, for

whom other factors such as working hours and work colleagues dilute the importance of pay

in itself, and by extension the resulting change from the original action bundles for the two

workers will likely be different. The second, relative position, is especially relevant for the

‘arm’s length’ suggestion Lazear makes as a way of mitigating actual (as opposed from

intended) sabotage. Similar to Adams’ 1965 Equity Theory, pay’s significance can be impacted

if it does not give feedback on how successful they have been in relation to others in the

workplace.10 So if an employee is constantly being paired off against other workers in distant

sectors of the firm with whom they cannot relate, they may lose interest in the outcome of the

competitions. The third, control, refers to power, such as how effective one has been in

influencing the behaviour of others. Again, as with the first example, assume two workers have

entered into a pay structure based on the outcomes of competitions having initially been paid

hourly. If the original hourly wage agreement was reached as a result of negotiation between

the employee or their union and management, then this power will have been lost once the

change to a tournament structure has been made. This is especially the case given that more

than once in his paper, Lazear calls for manipulation of the wage spread to produce the most

efficient outcome for the firm, with employees themselves not taken into account with regards

to the effects of possible wage cuts for lesser productive workers. Finally, pay can be

10 This theory comparison was chosen to reflect the example of General Motors given by Lazear. An alternative

theory (‘Goal Setting Theory’) stresses the role of dieback in increased performance.

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meaningful if it affects a person’s ability to acquire goods and services, but also vice -versa

(this was covered in greater detail on page 7 with reference to pay satisficing). Thus, if varying

numbers of these four criterion are filled – for Lazear’s paper, they are mostly not – then

workers may be so disengaged from their job that changes in pay in general and the wage

spread in particular may not have predicted or desired effects on worker actions.

A final critique is that of specific sabotage in competitions involving more than two players.

Examined formally on page 9, Lazear describes sabotage as a ‘public bad’ whereby all other

players are equally negatively impacted by a decision for one player to use sabotage. But in

their 1995 paper ‘Modeling Negative Campaigning’, Skaperdas and Grofman show this as not

being the case in sabotage in elections in the form of negative campaigning. The 1992 United

States Presidential Election for instance, chosen for being the standalone election of its kind

where three11 candidates could be seen as ‘players’ (having lead in the polls at least once),

sabotage was seen as targeted, rather than a blanket reduction in the output of other players

(Skaperdas and Grofman, 1992, p.56). Despite being well funded and on the ballot in all 50

states, Ross Perot over time lost his status of an equal with Bush and Clinton (recall that Lazear

models three worker competitions as between three identical workers, at least it is assumed this

was the case before the start of the competition) as his campaign developed. Yet in spite, or

perhaps because of this, ‘both Bush and Clinton appeared reluctant to attack Perot’ (Ibid). Of

course, this does not mean that the competition was sabotage free – all candidates behaved in

a similar way to competitions Lazear posited, with all three candidates allocating a proportion

of their funds to positive campaigning and negative campaigning/‘attack ads’.12 Yet a vote

‘taken’ from Perot by either Bush or Clinton as a result of their negative campaigning/sabo tage

against Perot would be just as valid as a vote taken from the other candidate. In their paper,

Skaperdas and Grofman conclude that it was ‘better to let sleeping dogs lie and feared that

Perot… would retaliate with direct attacks on the candidate who first attacked him’. Therefore,

whilst formally multi-competitor situations are simply an extension of two player competitions,

in reality player actions are not likely to be as simple to deduce.

11 In every other presidential election in the preceding 75 years, no third party candidate had been as successful

as Perot. It is with this distinction that he can be seen as ‘truly’ participating in the contest on the same level as

Bush and Clinton 12 These can be matched with notation in Lazear’s model with action, effort and sabotage respectively

15

CONCLUSION

Edward Lazear’s 1989 paper on sabotage in competition concludes with the statement ‘it is

often useful to pay workers on the basis of their relative performance’. If one can feasibly

conceive of a firm where all workers are similar enough to put into one of only several

‘groupings’, or for all intents and purposes, are indeed identical in their cost function, margina l

willingness to supply action, sabotage, effort, the effect that a change in their wage will have

on them, utility derived from utility of friendship, and that ‘[T]he morale of high-qua lity

workers… likely… be[ing] adversely affected by pay that regresses towards the mean’ is

eclipsed by increases in efficiency by a reduction in sabotage, and that the firm is introduc ing

performance- linked pay for one time period, then his workings and conclusions would be

accurate and this concluding statement strongly supported. Yet the complex nature of ‘politics

of the workplace’, a result of its ‘great importance to businessmen’ yields situations where such

axioms are frequently violated. Moreover, exploration of simpler but more fundamenta l

notions, such as potential costs for workers being caught by management sabotaging their

opponents, being omitted to emphasise more minor points such as the unworkable ‘personality

contingent wages’ is perhaps regrettable.

Yet whilst Lazear makes such excessive assumptions and leaves many points unexplored, as

Vandergrift and Yavas remark in their 2010 paper ‘An Experimental Test of Sabotage in

Tournaments’; ‘Lazear is the first paper to consider tournament competition when tournament

participants may take costly actions to lower the performance of their competitors (i.e.,

sabotage)’ (Vandergrift & Yavas, 2010). Whilst his patchy attempts with several of his

examples to move the paper from the theoretical to the contemporary are largely in vain, he

nevertheless sets out the hypothetical groundwork for expansion by others such as Chen [2003]

and the framework needed for empirical research by Drago and Garvey [1998], Harbring et al.

[2004] and Harbring and Irlenbusch [2005] (Ibid).

Finally, perhaps without realising it, Lazear has added another, helpful link between theoretica l

economics and modern life. Whilst his examples are that of firms such as General Motors and

terms such as ‘aspiring young executives’ makes an appearance as early as the second line,

such models concerning competitions and allocation choices between work and sabotaging

ones opponent are relatable to politics, sport and any other relatable scenario. It is therefore

with much encouragement that we observe Lazear publishing more articles in this field since

1989, and he is rightly commended as the founder of personnel economics.

16

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