Strongly Consistent Mechanisms

Abstract

In this chapter, we examine mechanisms that have strong Nash equilibria for any preference profile. We start with some examples (Section 5.1), then investigate in more detail a strongly consistent mechanism with tokens (Section 5.2). Section 5.3 addresses the issue somewhat more theoretically. In particular, we show that for any maximal blocking B, there exists a mechanism whose set of equilibrium outcomes coincides with the core of the blocking B. Further (Section 5.4) we consider direct core mechanisms, that is SCFs whose outcomes are in the core. The existence of a strongly consistent selector from the core depends on a property of the underlying blocking, namely “lam-inability”. In Section 5, we introduce several equivalent characterizations of laminable blockings, in particular an elimination procedure for finding strong Nash equilibria. Then (Section 5.6) we provide examples of laminable blockings and in Section 7, formulate a necessary and sufficient condition for lam-inability in terms of the blocking relation itself. In Section 8, we tackle the case of neutral laminable blockings. The Appendix provides insights on the strong implementation issue.