The optimal design of round-robin tournaments with three players

We study the optimal design of round-robin tournaments with three symmetric players. We characterize the subgame-perfect equilibrium in these tournaments with either one or two prizes. Our results show that the players who wish to maximize their expected payoffs or their probabilities of winning have different preferences about the order of games under tournaments with one or two prizes. We analyze the optimal allocations of players for a designer who wishes to maximize the players’ expected total effort in the tournaments with one and two prizes, and by comparing between them, it is demonstrated that in order to maximize the players’ expected total effort the designer should allocate only one prize.