Existence of Myopic-Farsighted Stable Sets in Matching Markets

We consider decentralized one-to-one matching markets with myopic and farsighted agents. We study myopic-farsighted stable sets that are internally and externally stable when myopic agents only care about their immediate payoffs, while farsighted agents take into account further possible reactions and care about their long-run payoffs when considering possible deviations. We constructively prove the existence of myopic-farsighted stable sets for any problem where there are farsighted agents only on one side of the market, while there may be myopic agents on both sides. We prove that a myopic-farsighted stable set may not exist when there are farsighted agents on both sides of the market and there is at least one myopic agent. Our analysis is in contrast to the earlier literature which considers only the extreme cases where either all agents are myopic, or all agents are farsighted, or all agents on one side are myopic and all agents on the other side are farsighted. Our results have several implications pertaining to core-stability and singleton stable sets, and yield numerous results from the literature as immediate corollaries. Finally, we extend several results to weakly stable sets and to many-to-one matching markets.