RISK TAKING IN CONTESTS AND THE ROLE OF CARROTS AND STICKS

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. …