Reciprocating Preferences in Matching Markets

Agents with reciprocal preferences prefer to be matched to a partner who also likes to collaborate with them. We introduce and formalize reciprocal preferences, apply them to matching markets, and analyze implications for mechanism design. Formally, we allow an agent's preferences to depend on the preferences of its potential partners, about which that agent has imperfect information. We show that there is no stable mechanism in standard two-sided markets. Observing the final allocation of the mechanism enables agents to learn about each other's preferences, which leads to instability. In a school choice setting where one side of the market is non-strategic, modified versions of the deferred acceptance mechanism achieve stability. These results contribute to the understanding of non-standard preferences in matching markets and their implications for efficient information and mechanism design.

Building on the theoretical framework, we also empirically investigate whether agents' preferences are subject to the information about others' preferences. Through a pre-registered and theory-guided laboratory experiment, we provide evidence that reciprocal preferences exist, that they substantially increase instability in matching markets, and that they have both preference-based and belief-based underpinnings.

[Preregistered in the AEA Registry #0007551] [https://doi.org/10.1257/rct.7551]