Abstract:

In 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 show that a rematching-proof equilibrium exists. Moreover, we extend these two results to the strong equilibria. Furthermore, the Nash equilibria in Roth [11] are shown to be rematching-proof equilibria. The relation between the rematching-proof equilibria and the strong equilibria is discussed as well.

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