STABLE MATCHINGS AND REMATCHING-PROOF EQUILIBRIA IN A 2-SIDED MATCHING MARKET

Tn this paper we introduce the notion of a rematching-proof equilibrium for a two-sided matching market to resolve Roth's open question: What kind of equilibria of the game induced by any stable mechanism with respect to misreported profiles produce matchings that are stable with respect to the true profile. We show that the outcome of a rematching-proof equilibrium is stable with respect to the true profile, even though the equilibrium profile may contain misreported preferences. We also show that a rematching-proof equilibrium exists. Moreover, the Nash equilibria in Roth (J. Econ. Theory 34 (1984), 383-387) are shown to be rematching-proof equilibria. (C) 1995 Academic Press, Inc.