Tournament Theory - Basic Model, Theoretical Implications, and Empirical Evidence

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University of Wisconsin-Milwaukee 1. Introduction Department of Economics A major branch of Labor Economics studies wage determination while particularly focusing on the underlying work relationships. Standard economic theory predicts that wages are equal to the value of the marginal product. In recent years, however, more attention has been paid to alternative compensation schemes that take account of the specific attributes characterizing labor markets. Tournament Theory - Basic Model, Impli- AsLAZEAR (1979) points out, work relationships can ultimately be typified as a Principle Agent situation between employers who do not have cations, and Empirical Evidence

perfect information about their workers’ level of effort and employees who derive additional utility from shirking. Different from standard economic belief workers’ pay can therefore deviate from their marginal utility, thus creating inefficiencies. One possible solution discussed in

by

the literature is the work-life incentive scheme that withholds part of the worker’s pay early in a person’s professional career and rewards

Denis Drechsler

loyal behavior by continuously increasing wages with tenure.

Other studies have concentrated on tournament-type compensation schemes (see, e.g., LAZEAR/ROSEN, 1981; GREEN/STOKEY, 1983; NALEBUFF/STIGLITZ, 1983; MALCOMSON, 1984; ROSEN, 1986; BULL et al., 1987). Though related to work-life incentive schemes, tour-

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Tournament Theory - Basic Model, Implications, and Empirical Evidence Tournament Theory - Basic Model, Implications, and Empirical Evidence

nament theory offers a different insight into the means by which firms promotion schemes in academic professions. Furthermore, tournament can motivate and control their workers. Different from wage contracts, theory can help to understand the processes that determine the electournament theory emphasizes the interpersonal comparison between tion of political leaders. Another prominent field where tournament theworkers as a means to determining a worker’s pay. It depicts promotions ory is employed and empirically tested is sports, where the quality of and wages as resulting from sequential elimination tournaments within performance allegedly depends upon the overall prize-money that can be the firm, while a finite amount of prizes are awarded according to a won. In fact, many researchers believe that professional sports may be person’s relative output. Consequently, the goal for an employee is not the only realm that allows an empirical application of tournament theory only to perform well, but primarily to do better than the others. As (i.e. ALCHIAN, 1988).

LAZEAR and ROSEN (1981) show in their seminal paper on rank-order Starting with Lazear and Rosen’s basic model this paper gives an over- pre-fixed remuneration schemes can be a very efficient view of the existing literature that empirically tests tournament theory.

device for a firm to overcome the Principle Agent problem. Especially The rest of the paper is structured as follows: section 2 sketches the

when measuring individual output is costly or impossible tournaments assumptions and main predictions of basic rank-order tournaments; sec- other compensation schemes; they may even be inevitable if tion 3 examines the existing literature on tournament theory and pre- in a particular firm are indivisible. sents results from experimental studies as well as empirical findings Tournament theory generates incentive-based predictions about wage from professional sport, academia, and private corporations; section 4 structures across the firm. Because an agent’s payoff only depends upon concludes.

his or her relative performance, tournament theory proposes an incen- 2. Basic Model

tive mechanism that is quite distinct from individual incentive schemes,

Tournament theory is largely inspired by the observation that workers such as piece rates. In the literature, tournaments have been proposed

in hierarchical organizations are paid wages tied to their rank rather as an explanation for the high pay and large fluctuation of CEOs. It is also used to analyze the reward system of sales-based jobs and the

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Tournament Theory - Basic Model, Implications, and Empirical Evidence Tournament Theory - Basic Model, Implications, and Empirical Evidence

than the value of their marginal product. Essentially, all models of tour-

(2) ² nament theory are composed of the following elements:

∞ −

where ξ represents the distribution function of (ε 2 -ε 1 ). Effort costs

• a certain number of people compete for a limited and fixed set C(µ i ) are assumed to be strictly increasing while the utility functions are of prizes and rewards, while the size of each prize depends upon its relative rank (first prize > second prize > third prize

linear so that: etc.) & [ ] • the rank ordering is the ultimate distinguishing factor be- [ ] µ − = − µ (3) − = − ) ( ) ( C w C w U ) ( ) ( C w C w U

i L i L tween prizes i H i H

• prizes can be promotions, benefits, bonuses etc.

as workers are assumed to be risk neutral. In their paper, Lazear and Rosen consider a model of two identical The effort of each worker thus depends on the noise level that influworkers (i= 1,2) who compete for promotion for a higher wage (w H > w ^L ences expected utility. The noisier the effort-productivity relationship, while w H + w L completely exhausts the firm’s revenue) on the basis of the less effort the worker will invest. On the other hand, given an optitheir relative production levels. Each worker’s output depends on his or mal price differential (w H - w L ), a tournament can mimic the incentive her own level of effort (µ i ) and a random error (ε i with mean zero and effect of piece rates that directly measure individual output. In some variance σ ² ) that the workers do not know at the time they choose their circumstances, a tournament can thus be a very effective alternative level of effort (noise). When p denotes the probability of winning the for a firm to promote and reward its worker’s level of effort solely base tournament the worker has to maximize his or her expected utility in upon relative performance. As relative performance usually will be easthe following way:

ier to measure, the advantages for the firm become apparent. [ ] [ ] (1) max µ − ∗ − + − ∗ = e ) ( ) 1 ( ) ( ) ( C w U p C w U p U

i L i H i

As shown in the paper, workers too will sometimes derive additional util-The probability of individual 1 to win at a Nash equilibrium where work- from working in a tournament environment. Generally, a worker can

ers are identical and the supplied level of effort µ i equals µ 1 and µ 2 is:

decide between three different compensation schemes: a linear piece

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Tournament Theory - Basic Model, Implications, and Empirical Evidence Tournament Theory - Basic Model, Implications, and Empirical Evidence

rate, a fixed standard, and a tournament. In the first, each worker’s randomness in the opponent’s output is due largely to the error term. On compensation is directly tied to output; in the second, each worker is the other hand, it will only introduce additional noise into the wageawarded a particular prize depending on whether the person’s output effort-relationship if this is not the case. Relative compensation lies above or below a specified standard; in the third, the agent receives schemes that base a worker’s reward on his or her performance as well a prize according to rank-order. as on the performance of his colleagues take advantage of the fact that the vector of output levels for the whole group is a source of informa-Lazear and Rosen show that if the workers are risk neutral, the moral

tion about the common shock - which by assumption the principal cannot hazard problem (i.e., shirking) can be costlessly avoided by shifting all

observe directly.

risks to the workers. If workers are risk averse, the relative ranking of the three schemes depends upon the relative variance of the error term The 1-period model can easily be expanded to n-periods (ROSEN, 1986). In a tournament with n-rounds and initially 2 ⁿ competitors Rosen shows and the importance of the stochastic component of the output contributed to effort. If the variance of the error term is relatively large, a that the prize-increase for the n-1 winners can be constant, while the increase for the winner of the last round must be disproportionately tournament will outperform the other schemes; if the variance of the component of output attributed to effort is large, one of the other two higher. He believes that the prospect of receiving a promotion to a more schemes will dominate. prestigious and higher paying position and the opportunity of further tournament competition creates higher incentives among lower level In a similar work, GREEN and STOKEY (1983) examine why a tournament

managers. More specifically, since successfully finishing a round not only performs well when the error term is important, and rather poor when it

contains the benefit of winning the associated prize, but also includes is unimportant. They argue that competing in a tournament is like being

the expected value of future rewards, the tournament winner needs to judged against a standard which resembles a random variable (the oppo- compensated for the lack of expected utility from future competinents output). This is useful if the random standard is highly correlated

tion.

with the random component of the agent’s own output, that is when the

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Tournament Theory - Basic Model, Implications, and Empirical Evidence Tournament Theory - Basic Model, Implications, and Empirical Evidence

This idea can explain why wages for persons at the very top of a hierar- 3. Testing Tournament Theory

chical organization are disproportionately high. It also sheds some light

Empirical studies have only found mixed evidence of the main predic- the fact that often times wage increases come with promotion. Fur- of tournament theory. A serious bottleneck of all econometric

thermore, tournament theory offers a scientific explanation for the

models that try to test tournament theory in a real world situation is

high turn-over rate of CEOs and the reasons why top managers are usu- lack of relevant data. Although the general predictions of tourna- granted large severance packages to make up for the limited time

ment theory seem to hold, many important implications of tournament

they can stay in office. In order for a rank-order tournament to func- are often times not testable in an organization context. The em- smoothly new incentives constantly need to be provided; that is, a

pirical evidence of tournament theory is thus scattered around some

tournament must always open promotion opportunities for new-comers.

very diverse areas which makes it hard to derive a complete and coherent picture. Still, researchers have found support of a positive relation-Generally, the predictions of tournament theory can be summarized as ship between promotion rates and wage growth. Several studies have

follows:

also confirmed the existence of a disproportionate wage increase for

a) firms generate incentives by having a pre-fixed remuneration scheme top managers. Moreover, the convexity assumption of pay with level of b) the noisier the effort-output relationship the less effective rank finds some support in the literature. the tournament c) the relative performance of individuals depends upon the to-The following section gives an overview of the existing literature that tal prize money

has empirically tested tournament theory. Studies are mainly divided d) promotions matter for an individual’s earnings profile

into three categories: (i) experimental studies, (ii) professional sports, e) the prize for the overall winner of a tournament must be

and (iii) studies on the corporate level.

disproportionately high

The following sections gives an overview of studies that have empirically tested these predictions.

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