Double Round-Robin Tournaments

A tournament is a simultaneous n-player game that is built on a two-player game g. We generalize Arad and Rubinstein’s model assuming that every player meets each of his opponents twice to play a (possibly) asymmetric game g in alternating roles (using sports terminology, once "at home" and once "away"). The winner of the tournament is the player who attains the highest total score, which is given by the sum of the payoffs that he gets in all the matches he plays. We explore the relationship between the equilibria of the tournament and the equilibria of the game g. We prove that limit points of equilibria of tournaments as the number of players goes to infinity are equilibria of g. Such a refinement criterion is satisfied by strict equilibria. Being able to analyze arbitrary two-player games allows us to study meaningful economic applications that are not symmetric, such as the ultimatum game.