Optimal prize allocations in group contests
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Optimal prize allocations in group contests Francesco Trevisan1 Received: 29 March 2019 / Accepted: 5 March 2020 © The Author(s) 2020
Abstract We characterize the optimal prize allocation, namely the allocation that maximizes a group’s effectiveness, in a model of contests. The model has the following features: (i) it allows for heterogeneity between and within groups; (ii) it classifies contests as “easy” and “hard” depending on whether the marginal costs are concave or convex. Thus, we show that in an “easy” contest the optimal prize allocation assigns the entire prize to one group member, the most skilled one. Conversely, all group members receive a positive share of the prize when the contest is “hard” and players have unbounded above marginal productivities. If the contest is “hard” and the marginal productivities are bounded above, then only the most skilled group members are certain of receiving a positive share of the prize for any distribution of abilities. Finally, we study the effects of a change in the distribution of abilities within a group. Our analysis shows that if the contest is either “easy” or a particular subset of “hard”, then the more the heterogeneity within a group, the higher its probability of winning the prize.
1 Introduction “Soldiers generally win battles; generals get credit for them.”1 Contests are ubiquitous in that they arise, for example, in wars, sports, electoral campaigns and workplace competitions. When contests arise between groups,
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Napoleon (1769–1821).
I would like to thank Ed Hopkins, Santiago Sanchez Pages, Tatiana Kornienko, Jozsef Sakovics, Ina Taneva, Andrew Clausen, Marco LiCalzi, Alessandro Spiganti; audiences at the 2016 CBESS Conference on Contests: Theory and Evidence in Norwich; and the 2016 International Conference on Game Theory at Stony Brook University. This work was supported by the Economic and Social Research Council grant number ES/J500136/1. * Francesco Trevisan [email protected] 1
The University of Edinburgh, Edinburgh, UK
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respective members win or lose the prize collectively. However, individuals in a group may have different positions, skills, prize valuations, and various impacts over the outcome of the competition. When the prize has private characteristics, this within group heterogeneity can lead to personalized incentives, such as highly skilled players receiving a higher share of the prize over lower skilled ones. Conversely, an egalitarian allocation of prizes may be used to encourage cooperative behaviours among members. At the beginning of the Republic of Rome, for example, the tribunes equally distributed the spoils of war among all army members, including those who only guarded the settlements and protected the wounded. After 407 BC, the Roman Senate introduced different incentives according to the roles performed by the members of the army: ordinary soldiers received a third of the wage of the knights and half of the wage of centurions. A similar rule was used under Napoleon’s Empire. No
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