First-Mover Advantage in Round-Robin Tournaments

We study round-robin tournaments with one prize and four symmetric players. There are three rounds, each of which includes two sequential matches where each player plays against a different opponent in every round. Each pair-wise match is modelled as an all-pay auction. We characterize the sub-game perfect equilibrium and show that a player who plays in the first match of each of the first two rounds has a first-mover advantage as reflected by a significantly higher winning probability as well as a significantly higher expected payoff than his opponents. Therefore, if the contest designer wishes to sustain the fair play principle he has to schedule all the matches in each round at the same time in order to obstruct a meaningful advantage to one of the players.