Existence of Myopic‐Farsighted Stable Sets in Matching Markets

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 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, yielding coalitional myopic‐farsighted stable sets, and to settings where not all members of an enforcing coalition must strictly gain, yielding myopic‐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.