Bipartisan set: Difference between revisions
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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. |
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 journal|last=Laffond|first=G.|last2=Laslier|first2=J.F.|last3=Le Breton|first3=M.|date=Jan 1993|title=The Bipartisan Set of a Tournament Game|url=https://linkinghub.elsevier.com/retrieve/pii/S0899825683710109|journal=Games and Economic Behavior|language=en|volume=5|issue=1|pages=182–201|doi=10.1006/game.1993.1010|via=}}</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]]. |
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== References == |
== References == |
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Latest revision as of 22:38, 5 April 2020
The bipartisan set:
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.[1]
It can be found by using techniques for solving zero-sum games to find the solution for the zero-sum game which is found from the margins-based pairwise counting matrix.
References
- ↑ Laffond, G.; Laslier, J.F.; Le Breton, M. (Jan 1993). "The Bipartisan Set of a Tournament Game". Games and Economic Behavior. 5 (1): 182–201. doi:10.1006/game.1993.1010.