Consistency in finite strategic games with at most 2 players

Abstract

In the paper by [5] it was proved a characterization of the Nash equilibrium correspondence in terms of consistency, converse consistency and one-person rationality. It was also showed that, in general, perfect and proper equilibrium correspondences do not satisfy consistency. [3] proposed a characterization of the Nash equilibrium correspondence, for the class of mixed extension of finite games, in terms of non-emptiness, utility maximizing for one-person games, and consistency. As a consequence of their result, the nonempty refinements which extend the idea of utility maximization for one-person games do not satisfy consistency. It is well-known that refinements of the Nash equilibrium correspondence exhibite particular properties in the class of mixed extension of two-person games. We investigate the compatibility of several refinements of the Nash equilibria set with consistency, one-person rationality and non-emptiness for this class of games.