The optimal prize structure of symmetric Tullock contests

We show that the optimal prize structure of symmetric n-player Tullock tournaments assigns the entire prize pool to the winner, provided that a symmetric pure strategy equilibrium exists. If such an equilibrium fails to exist under the winner-take-all structure, we construct the optimal prize structure which improves existence conditions by dampening efforts. If no such optimal equilibrium exists, no symmetric pure strategy equilibrium induces positive efforts

Sequential All-Pay Auctions with Head Starts and Noisy Outputs

We study a sequential (Stackelberg) all-pay auction with two contestants who are privately informed about a parameter (ability) that affects their cost of effort. Contestant 1 (the fi?rst mover) exerts an effort in the fi?rst period, while contestant 2 (the second mover) observes the effort of contestant 1 and then exerts an effort in the second period. Contestant 2 wins the contest if his effort is larger than or equal to the effort of contestant 1; otherwise, contestant 1 wins. We characterize the unique subgame perfect equilibrium of this sequential all-pay auction and analyze the use of head starts to improve the contestants' performances. We also study this model when contestant 1 exerts an effort in the fi?rst period which translates into an observable output but with some noise. We study two variations of this model where contestant 1 either knows or does not know the realization of the noise before she chooses her effort. Contestant 2 does not know the realization of the noise in both variations. For both variations, we characterize the subgame perfect equilibrium and investigate the effect of a random noise on the contestants' performance.Sequential all-pay auctions, head starts, noisy outputs.

The optimal prize structure of symmetric Tullock contests

We show that the optimal prize structure of symmetric n-player Tullock tournaments assigns the entire prize pool to the winner, provided that a symmetric pure strategy equilibrium exists. If such an equilibrium fails to exist under the winner-take-all structure, we construct the optimal prize structure which improves existence conditions by dampening efforts. If no such optimal equilibrium exists, no symmetric pure strategy equilibrium induces positive efforts.Tournaments; Incentive structures; Rent seeking

Eyes on the Prize: Increasing the Prize May Not Benefit the Contest Organizer in Multiple Online Contests

Given the proliferation of online platforms for crowdsourcing contests, we address the inconsistencies in the extant literature about the behavioral effects of increasing the prize awarded by contest organizers. We endeavor to resolve these inconsistencies by analyzing user behavior in a highly controlled experimental setting in which users can participate (by exerting real effort rather than stated effort) in multiple online contests that vary only in their prizes. The analysis of the behavior of 731 active participants in our first experiment showed that both participation and effort were non-monotonic with the prize, that the low-prize contest was the most effective for the organizers, and that increasing the prize of the low-prize or high-prize contest by 50% actually decreased the benefits for organizers. Our findings advance theory by providing insight into when and why extrinsic incentives fail to produce the desired effects in crowdsourcing contests

Heterogeneous risk/loss aversion in complete information all-pay auctions

We extend previous theoretical work on n-player complete information all-pay auctions to incorporate heterogeneous risk- and loss-averse utility functions. We provide sufficient and necessary conditions for the existence of equilibria with a given set of active players with any strictly increasing utility functions and characterize the players’ equilibrium mixed strategies. Assuming that players can be ordered by their risk aversion (player a is more risk-averse than player b, if whenever player b prefers a certain payment over a given lottery, so does player a), we find that in equilibrium, the more risk-averse players either bid higher than the less risk-averse players and win with higher ex-ante probability – or they drop out. Furthermore, while each player’s expected bid decreases with the other players’ risk aversion, her expected bid increases with her own risk aversion. Thus, increasing a player’s risk aversion creates two opposing effects on total expected bid. A sufficient condition for the total expected bid to decrease with a player’s risk aversion is that this player is relatively more risk-averse compared to the rest of the players. Our findings have important implications for the literature on gender differences in competitiveness and for gender diversity in firms that use personnel contests for promotions