On the Inconsistency of Equilibrium Refinement∗

Consistency and optimality together with converse consistency provide an illuminating and novel characterization of the equilibrium concept (Peleg and Tijs, 1996). But (together with non-emptiness) they preclude refinements of the equilibrium notion and selection of a unique equilibrium (Norde et al., 1996). We suggest two escape routes: By generalizing the concept of strict equilibrium we question the practical relevance of the existence requirement for refinements. To allow for equilibrium selection we suggest more complex reduced games which capture the inclinations of “players who already left”. ∗The author is thankful for comments by Martin Dufwenberg, Jörg Oechssler and Klaus Ritzberger and the constructive advice of two anonymous referees and the editor in charge. †Max Planck Institute for Research into Economic Systems, Strategic Interaction Group, Kahlaische Str. 10, 07745 Jena, Germany