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Article Excerpt
I. INTRODUCTION
When individuals compete for promotions, bonuses, or other rewards tied to their relative performance ranking vis-a-vis other contestants, competition is likely to drive not just work effort but, where imperfect monitoring permits, other choices at the contestants' discretion. In this article, we ask how rank-dependent compensation influences attitudes toward risk, or the choice of variance of output, when contestants have opportunities to influence this aspect of their output distribution. Unlike previous literature, we assume that it is costly for contestants to alter the variance of output and that identical contestants simultaneously choose both the mean of their output distribution (i.e., work effort) and its variance. Our analysis emphasizes the importance of the number of players and symmetry (or lack thereof) of payoffs on contestants' incentives.
We find that contestants will engage in risk seeking (increasing the variance of their output distribution) in contests among three or more players when the payoff structure offers a greater prize for ranking first than the penalty for ranking last, as happens in winner-take-all contests. If the tournament organizer or sponsor values the aggregate output of the contestants, as is typically assumed in labor market tournaments, this risk-seeking behavior is inefficient because it is costly but does not increase the expected output. However, we argue that many contests, such as the research and development tournaments first modeled by Taylor (1995), may be characterized by an organizer who cares only (or primarily) about the highest output achieved by a single contestant (e.g., the best submission received). In such cases, the organizer may benefit from costly risk taking among contestants. We show that three payoff levels--a prize to the contestant ranked first, a penalty to the contestant ranked last, and a common intermediate payoff to all others--are sufficient to achieve any combination of effort and variance of output that the organizer wishes to induce among contestants, so long as the desired output variance does not exceed that which results from a winner-take-all prize structure. Therefore, the sponsor's problem can be characterized as choosing the optimal mean and variance of the output distribution given the contestants' costs of influencing the mean and variance of output. In this way, our model provides an explanation for the importance of both carrots (prizes) and sticks (penalties) in competitive settings.
Only through the combined use of both can a contest organizer determine the effort and the variance of output chosen by contestants, and doing so is necessary to achieve optimal performance from contests.
Since the pioneering work of Lazear and Rosen (1981), Nalebuff and Stiglitz (1983), O'Keeffe, Viscusi, and Zeckhauser (1984), and others, rank-order tournaments or contests have been used to model incentives in a variety of economic settings. In particular, executive compensation has frequently been modeled as a tournament in which low-level executives are motivated by the prospect of climbing the corporate ladder and obtaining the large salaries attendant to top-ranking executives, as in Rosen (1986) and Bognanno (2001). Similarly, the behavior of investment fund managers who compete for top fund rankings has been modeled as a tournament by Brown, Harlow, and Starks (1996). Taylor (1995) developed a model of research tournaments in which contestants search for an innovation, and the best innovation submitted to the sponsor wins a prize. The distinguishing feature of a tournament or contest is that contestants are paid based on the rank of their output relative to others rather than the level of output. Prize levels are set in advance and competition to win generates the incentive to exert effort to increase output.
Lazear and Rosen (1981) showed that rank-order tournaments can provide an efficient incentive framework in a labor market setting when workers are risk neutral. A substantial literature has explored the costs and benefits of tournaments relative to other incentive schemes, such as piece rates, with regard to such factors as the risk aversion of workers and the flexibility of the incentive framework to environmental uncertainty (e.g., Nalebuff and Stiglitz 1983; O'Keeffe, Viscusi, and Zeckhauser 1984). More recent work has begun to explore incentives in competitive settings when contestants choose not solely how much work effort to exert, but some other aspect of the work that is undertaken. For example, executives in workplace tournaments may have substantial scope for influencing the output variance, or risk, of projects they undertake. They may also be able to influence the mean output through choices other than work effort, such as by choice of production process or regulatory compliance. (1) When monitoring is imperfect, it is likely that workers' incentives will not be perfectly aligned with those of their employer (the contest organizer) because they will have opportunities to increase their probability of winning by engaging in activities which do not serve the interest of the firm.
The literature on risk taking in tournaments or contests has developed along several different lines. (2) Bronars (1987) was the first to address risk-taking incentives induced by a tournament and showed that leaders in sequential tournaments have an incentive to be risk averse while followers are risk seeking. This result illustrates the important effect that asymmetry among players can have on risk taking, an insight which has been developed in later articles. Tsetlin, Gaba, and Winkler (2004) study multiround contests in which a single winner is determined by the best overall performance. They find that it is optimal for players to choose a higher variance strategy at a given point in the game if their results to that point have been fairly poor (relative to the distribution of possible outcomes) and to choose a lower variance strategy if their results have been relatively good. However, they do not model players as choosing effort; players choose only the variance of output, which can be adjusted at no cost. Krakel and Sliwka (2004) consider asymmetric two-player tournaments in which players first choose a high-or low-risk strategy then choose effort. In this setting, they show that diverse equilibria are possible with the player holding the advantage not necessarily choosing lower variance than the disadvantaged player. The equilibrium depends on the magnitude of the ability difference, the shape of the cost function, and the magnitude of the prize spread.
Gaba, Tsetlin, and Winkler (2004) consider contests with identical contestants who can costlessly alter the variance of their output (but are unable to affect the mean). They assume that contests have a specified number of winners who each receive an identical payoff, while the remaining contestants receive an identical losing payoff. (3) Gaba et al. show that contestants have an incentive to increase variance when the number of winners is less than half the number of contestants and to decrease variance when the number of winners is more than half. Although the framework is different, the issue of whether the number of winners is greater or less than half the number of contestants and the effect this has on risk taking parallels our discussion in this article of the balance of the prize (carrot) and penalty (stick).
Hvide (2003) models a symmetric tournament in which contestants simultaneously choose both effort and risk. Hvide considers two-player tournaments in which contestants can costlessly alter the variance of their output. In his model, risk-taking incentives arise from the fact that the greater the variance of both players' outputs, the lower the incentive to exert work effort for both players. A player having increased the variance of his output does not directly increase the likelihood of his winning in the symmetric equilibrium of the game, but it reduces the effort both he and his opponent will exert in equilibrium. In this setting, if the variance of output is unbounded, the unique equilibrium involves both players choosing infinite variance and zero effort. When variance is bounded, players choose the maximum variance and a sufficiently high prize spread will generate efficient incentives just as in a standard tournament model; inefficiency arises in this case only if players are risk averse.
The model we develop is perhaps closest to that of Hvide (2003) in that we assume that each...
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