Existence of Myopic-Farsighted Stable Sets in Matching Markets

Abstract

In the context of one-to-one matching markets, we study myopic-farsighted stable sets, which are internally and externally stable when myopic agents consider the immediate payoffs from their deviations, while farsighted agents anticipate counter-deviations and consider their final payoffs. We constructively prove the existence of a (rational expectations) myopic-farsighted stable set, where farsighted agents receive a single payoff by always being matched with the same partners, while myopic agents may receive multiple payoffs. For myopic-farsighted weakly stable sets—where strict improvement is required only for some members of a deviating coalition—our results extend to many-to-one matching markets. As a key corollary, we provide a foundation for the outcome of the efficiency-adjusted deferred acceptance algorithm, showing that it forms a singleton myopic-farsighted stable set when one side is farsighted and the other is myopic.

Keywords: JEL Classification: C78, D70, J41, J44 Matching problems, stable sets, myopic and farsighted agents

JEL Classification: C78, D70, J41, J44