# Bipartisan set

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.