From winning strategy to Nash equilibrium (Q2922499)

This paper presents an alternative to Nash theorem, showing conditions on two-player normal form games for the existence of Nash equilibria. The basic tool is the use of the concept of determinacy of games (i.e. the existence of winning strategies in zero-sum games). The main argument of the paper starts by noting that any two-player normal form game can be transformed into a zero-sum one. The author proves that the ensuing winning strategies support a Nash equilibrium in the original game, provided that the preferential orderings over outcomes have uniform finite height or, if the action spaces are enumerable infinite, the lower contour sets constitute well-founded chains.