THE BIPARTISAN SET OF A TOURNAMENT GAME

A tournament is a complete asymmetric binary relation U over a finite set X of outcomes. To a tournament we associate a two-player symmetric zero-sum game, in which each player chooses an outcome and wins iff his outcomes beats, according to U, the one chosen by his opponent. We prove that the game has a unique mixed-strategy equilibrium. By considering the outcomes played at equilibrium we define a new solution concept for tournaments, called the Bipartisan Set. We prove some properties satisfied by this solution and explore the issue of its location with respect to the existing solutions in terms of inclusions and scores. © 1993 Academic Press, Inc.