If a connected component of perfect equilibria of a two-player game contains a stable set as defined by Mertens, then the component is itself stable. Thus the stable sets maximal under inclusion are connected components of perfect equilibria.

We extend the results of Blume, Brandenberger, and Dekel (1991b) to obtain a finite characterization of perfect equilibria in terms of lexicographic probability systems (LPSs). The LPSs we consider are defined over individual strategy sets and thus capture the property of independence among...

Characterisations of stable equilibria in terms of the best reply correspondence are given. Copyright Springer-Verlag 2004