Existence of Myopic-Farsighted Stable Sets in Matching Markets

Abstract

In the context of one-to-one matching markets, we studymyopic-farsighted stable sets, which are internally and externally stable when myopic agents consider immediate payoffs from their deviations, while farsighted agents anticipate counter-deviations and consider final payoffs. We constructively prove the existence of a (rational expectations) myopic-farsighted stable set, in which farsighted agents receive a single payoff while myopic agents may receive multiple payoffs. Our existence result extends to settings with enforcing coalitions of arbitrary size, yieldingcoalitional myopic-farsighted stable sets, and to settings where not all members of an enforcing coalition must strictly gain, yieldingmyopic-farsighted weakly stable sets. When all farsighted agents have unit demand, our results also extend to many-to-one matching markets. As a key corollary, we provide a foundation for the efficiency-adjusted deferred acceptance algorithm by showing that its outcome constitutes a singleton myopic-farsighted stable set when one side is farsighted and the other is myopic.