Existence of Myopic‐Farsighted Stable Sets in Matching Markets
2026-06-02
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.