Bipartisan set: Difference between revisions

The bipartisan set:<blockquote>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. <ref>{{Cite webjournal|urllast=https://www.semanticscholar.org/paper/The-Bipartisan-Set-of-a-Tournament-Game-Laffond-|first=G.|last2=Laslier/6de00a0986fb668bc947452eb8eeffeddd7979bf|first2=J.F.|last3=Le Breton|first3=M.|date=Jan 1993|title=The Bipartisan Set of a Tournament Game|lasturl=https://linkinghub.elsevier.com/retrieve/pii/S0899825683710109|firstjournal=Games and Economic Behavior|datelanguage=en|websitevolume=5|url-statusissue=live1|archive-urlpages=182–201|archive-datedoi=10.1006/game.1993.1010|access-datevia=}}</ref></blockquote>It can be found by using [https://en.wikipedia.org/wiki/Zero-sum_game#Solving techniques for solving zero-sum games] to find the solution for the zero-sum game which is found from the margins-based [[Pairwise comparison matrix|pairwise counting matrix]].