When farsighted agents enter matching markets, stability takes on new meaning

What happens to matching markets when participants look beyond immediate gains and anticipate the long chain of reactions their choices might trigger? This question becomes even more complex when couples submit joint preferences as in the residency matching problem where stable outcomes may not exist.

In the study “Matching Markets with Farsighted Couples”, our researcher Ata Atay, alongside with Sylvain Funck, Ana Mauleon and Vincent Vannetelbosch (UC Louvain) examine how farsighted behaviour affects stability in markets with couples. They use the concept of the farsighted stable set, which captures how farsighted agents anticipate the actions of other coalitions and evaluate sequences of strategic moves that may lead to a final matching.

Their central result is clear. A matching that is stable under traditional myopic preferences remains stable when agents are farsighted. A singleton matching forms a farsighted stable set exactly when the matching is stable. This extends previous findings in marriage and roommate markets to the more intricate setting of couples.

The authors also show that while a farsighted stable set cannot have exactly two matchings, larger sets with several non stable matchings may exist. These situations arise even in markets that offer at least one stable matching, revealing richer dynamics when agents look forward.

The study also explores markets with no stable matching. Some of these markets still admit farsighted stable sets, while others do not. To handle cases where farsighted stability fails, the authors propose the DEM farsighted stable set, a refinement that always exists and can guide predictions.

Their results also apply to markets where hospitals have several positions, provided that hospitals have responsive preferences. This ensures that the paper’s insights remain valid in more realistic environments.

The research contributes to a growing literature on how sophisticated reasoning shapes real matching outcomes. Introducing agents with different levels of farsightedness can destabilize classical matchings and stabilize alternatives such as those obtained from Top Trading Cycle Mechanism. The findings open new avenues for understanding complex matching environments such as in residency matchings problems around the globe (e.g. MIR in Spain, NRMP in the US, SFAS in Scotland) where couples play a central role.

Discover more about the UB School of Economics’ research! Explore the full list of our researchers and their latest research here.

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