A Simple Model of Competition Between Teams∗

We model a competition between two teams as an all-pay auction with incomplete information. The teams may differ in size and individuals exert effort to increase the performance of one’s own team via an additively separable aggregation function. The team with a higher performance wins, and its members enjoy the prize as a public good. The value of the prize is identical to members of the same team but is unknown to the other team. We show that there exists a unique monotone equilibrium in which everyone actively participates, and in this equilibrium a bigger team is more likely to win if the aggregation function is concave, less likely if convex, or equally likely if linear. We also show that if the aggregation function is concave or linear then the expected payoff for a player in the bigger team is higher than that in the smaller team. Finally, we investigate how teams may form endogenously.