Private-information group contests: Best-shot competition

Abstract

We model competing groups when players' values for winning are private information, each group's performance equals the best effort (“best shot”) of its members, and the group with the best performance wins the contest. At the symmetric equilibrium of symmetric contests, increasing the number of competing teams may increase or decrease each team's performance, but it unambiguously increases the overall expected best shot. Depending on the elasticity of the distribution of players' values, individual, team, and contest performance may increase or decrease with team size. Considering just two competing groups that differ only in size, we show members of the smaller group use the more aggressive strategy, but, depending on the nature of uncertainty, either team may be more likely to win. More generally, when teams' value cdfs differ, increasing one team's size decreases (increases) that team's chance of winning if its value cdf is elastic (inelastic).