First-mover advantage in round-robin tournaments

We study round-robin tournaments with either three or four symmetric players whose values of winning are common knowledge. With three players there are three rounds, each of which includes one pair-wise game such that each player competes in two rounds only. The player who wins two games wins the tournament. We characterize the subgame perfect equilibrium and show that each player’s expected payoff and probability of winning is maximized when he competes in the first and the last rounds. With four players there are three rounds, each of which includes two sequential pair-wise games where each player plays against a different opponent in every round. We again characterize the subgame perfect equilibrium and show that a player who plays in the first game of each of the first two rounds has a first-mover advantage as reflected by a significantly higher winning probability as well as by a significantly higher expected payoff than his opponents.