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Article Excerpt
I. INTRODUCTION
The use of promotion tournaments is fairly widespread, especially in the higher ranks of firms and organizations. The incentive property of tournaments has been studied earlier and extensively in the theoretical literature by Lazear and Rosen (1981); Green and Stokey (1983); Nalebuff and Stiglitz (1983); and O'Keeffe, Viscusi, and Zeckhauser (1984); for a survey, see McLaughlin (1988). The empirical studies, based on survey or experimental data, are fewer, and many survey analyses use sports data rather than business data (Prendergast 1999). These studies have confirmed that the efficiency of tournaments depends on the spread between the winner's and the loser's prizes, the number of prizes at stake, the size of the tournament, and the degree of uncertainty faced by the employees. (1)
However, both theoretical models and empirical studies also point to some factors that limit the incentive effect of tournaments, such as collusion among employees or employees sabotaging each other, as studied by Lazear (1989) in a theoretical analysis and experimentally by Harbring and Irlenbusch (2005). More generally, most laboratory experiments have provided evidence of tournaments being associated with a high variance in effort (see in particular Bull, Schotter, and Weigelt 1987; Harbring and Irlenbusch 2003; van Dijk, Sonnemans, and van Winden 2001). This variance of effort, which is found to be larger in tournaments than in an equivalent piece-rate scheme, reduces the overall efficiency of tournaments.
The principal aim of this article was to show that previous experimental evidence regarding the variability of effort in tournaments is misleading because the experiments have not accounted for sorting, that is, that agents typically choose to participate in a tournament. The large variability observed in earlier studies is explained by Bull, Schotter, and Weigelt (1987) by the game nature of the tournament, which requires the agents to elaborate a strategy that is more cognitively demanding than the maximizing behavior required by a piece-rate system. Indeed, in addition to the stochastic technology of production, the agents have to cope with strategic uncertainty. Bull, Schotter, and Weigelt (1987) showed that the variance of effort diminishes when the strategic uncertainty is reduced, for example, when the subjects know that they are faced with automatons that always select the same level of effort that is also common knowledge. The variance remains high, however, indicating that the discontinuities in the payoff functions themselves contribute to the difficulty of the maximization program and to the high variance of effort. More recent articles, such as Vandegrift and Brown (2003), have shown that the use of high-variance strategies may be related to both the difficulty of the task and the ability of the individuals. The hypothesis that we test in this article is that the variability of effort may be reduced--and thus the efficiency of tournament increased--by allowing people to choose their payment scheme, that is, providing them with a choice to enter the competition or not. More precisely, we suggest that the observed high variance of effort may be due to the fact that in previous experiments, a competitive payment scheme is imposed on very risk-averse or underconfident subjects. For example, facing uncertainty, some of the subjects drop out, that is, they choose the minimum effort, securing the loser's prize without bearing any cost of effort, whereas others choose the maximum effort, securing the winner's prize but at an inefficiently high cost of effort. Had the subjects been given the choice, like in flexible labor markets where people can choose to enter or shy away from competitive occupations, very risk-averse subjects would probably not have entered the competition and the overall variance of effort would be lower.
By testing whether the performance variability is reduced by the ex ante sorting effect of tournaments, our article contributes to a very recent literature about the importance of both incentive and sorting effects in the determination of payment schemes' efficiency, initiated by Lazear (2000). (2) This literature shows that sorting influences economic behavior. Earlier, the sorting function of tournaments has mainly been documented with respect to their ability to select ex post the best performers. However, their ex ante sorting effect is considerably less studied, and none of the previous empirical studies have been concerned with the impact of ex ante sorting on the variability of performance. (3)
To study the ex ante sorting effect of tournaments and its impact on the variability of effort, we have designed a laboratory experiment based on the comparison between a Benchmark treatment and a Choice treatment, involving 120 student-subjects. In the Benchmark treatment, half of the subjects are paid according to a piece-rate payment scheme and the other half enters pairwise tournaments. This treatment consists of a one-stage game in which the subjects choose their level of effort knowing their payment scheme and the uncertainty of the environment. We find, in line with earlier experiments, that in this treatment, the variance of effort is substantially higher in the tournament than in the piece-rate payment scheme. In the Choice treatment, we add a preliminary stage in which the subjects choose between a piece-rate scheme and a tournament. Those who choose the tournament are paired together. In the second stage, each subject decides on his level of effort. In both treatments, the individual outcome depends on both the effort level and an i.i.d, random shock. The difference between the two payment schemes emanates from the strategic uncertainty associated with the tournament setting.
By comparing the subjects' behavior in the two treatments, we can identify the impact of sorting on the average-level and the variance of effort. We also seek to identify determinants of self-selection. The equilibrium effort level is higher in the tournament than under the piece-rate scheme, but the expected utility of both compensation schemes is the same. Hence, risk-neutral subjects should be indifferent between the two schemes. For their part, risk-averse subjects can adopt a less risky scheme by choosing the piece-rate scheme. We measure the subjects' risk aversion using the lottery procedure proposed by Holt and Laury (2002).
Our experiment delivers three main findings. First, the key novel finding is that the employees' choice of pay schemes contributes to a considerable reduction in the variance of effort among contestants in the tournament. This result is confirmed by a robustness test in which the subjects are only allowed to choose their payment scheme in the first period of the game and for its whole duration. Second, the average effort is higher when the subjects can select their payment scheme in each period, which suggests that the sorting effect reinforces the incentive effect of both tournaments and variable pay schemes. Third, the subjects self-select according to their degree of risk aversion. A cluster analysis identifies a category of underconfident subjects and a category of hesitant ones who both tend to shy away from competition when they can choose their payment scheme. The resulting greater homogeneity of contestants improves the overall efficiency of tournaments. We conclude that in order to understand the origin of the high variance of effort in tournaments and, more generally, the efficiency of a payment scheme, recognition of heterogeneity of preferences is key.
The remainder of the article is organized as follows. Section II presents the theoretical framework and the experimental design. Section III gives the experimental procedures. Section IV describes and analyzes the experimental evidence. Section V discusses the results and concludes.
II. THEORY AND EXPERIMENTAL DESIGN The Model
Consider an economy with identical, risk-neutral agents. Agent i has the following utility function, separable in payment and in effort:
(1) [U.sub.i]([e.sub.i]) = u([p.sub.i]) - c([e.sub.i]).
with u([p.sub.i]) = concave and c([e.sub.i]) = convex.
The production technology is stochastic and output is increasing in the agent's effort:
(2) [Y.sub.i] = f([e.sub.i]) + [[epsilon].sub.i],
with f([e.sub.i]) = [e.sub.i] for the sake of simplicity and [[epsilon].sub.i] is an i.i.d, random shock distributed over the interval [-z, +z]. Only individual outcomes are observable and individual effort is not, neither by the principal nor by other agents. The cost function is increasing and is convex:
(3) c([e.sub.i]) = [e.sup.2.sub.i]/s,
with s > 0, c(0) = 0, c'([e.sub.i]) > 0, and c"([e.sub.i]) > 0. (4)
In the labor market, some firms pay the agents a piece-rate compensation scheme and other firms use tournaments. If there is a perfect mobility in the labor market at no cost, in the first stage, the agents choose their firm (i.e., their payment scheme) and in the second stage, they decide on their level of effort. Let us first solve the equilibrium effort levels under each mode.
In the piece-rate system, the agent's payment depends only on his own outcome. The payment consists of a fixed wage, denoted by a, corresponding to an input-based payment, and a linear piece rate, denoted by b, corresponding to an output-based payment. Under this compensation scheme, the agent's utility function becomes:
(4) [U.sup.PR.sub.i]([e.sub.i]) = a + [by.sub.i] - [e.sup.2.sub.i]/s.
The first-order condition is:
[delta][U.sup.PR.sub.i]/[delta][e.sub.i] = b- c'([e.sub.i]) = 0.
Thus, the equilibrium effort of each agent under the piece-rate payment scheme depends positively on the incentive, b, as well as the cost scaling factor, s:
(5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
In the firms practicing tournaments, the agents play a noncooperative game with incomplete information like in Lazear and Rosen (1981). In pairwise tournaments, two prizes are distributed: W is the winner's prize allocated to the agent whose outcome is the highest and L is the loser's prize, allocated to the other agent, with W > L. The magnitude of the difference between the two outcomes does not affect the determination of the winner of the tournament. The agent's utility is:
(6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
The agents being symmetric, the probability to win the tournament, pr([e.sub.i], [e.sub.j]), reduces to the probability that the difference in individual random terms exceeds the difference between individual effort levels: pr([e.sub.i], [e.sub.j]) = pr([[epsilon].sub.i] - [[epsilon].sub.j] > [e.sub.i] - [e.sub.i]). Agent i's expected utility of the tournament is:
(7) [EU.sup.T.sub.i]([e.sub.i], [e.sub.j]) = L + [pr([e.sub.i], [e.sub.j])(W - L)]-[e.sup.2.sub.i]/s.
The maximization program yields the following first-order condition:
(8) [delta][EU.sup.T.sub.i] ([e.sub.i], [e.sub.j])/[delta][e.sub.i] = [delta]pr([e.sub.i], [e.sub.j])/[delta][e.sub.i](W - L) - 2[e.sub.i]/s = 0.
We obtain a pure symmetric Nash equilibrium, where effort increases with the prize spread and decreases with both the cost of effort and the size of the shock distribution:
(9) [e.sup.T*.sub.i] = [e.sup.T*.sub.j]...
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