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Innovation and Entrepreneurship Research

Reciprocating Preferences in Two-Sided Matching

We introduce and study two-sided matching with reciprocating preferences and incomplete information on one side of the market. In the benchmark model, information is perfect and agents’ preferences are exogenously given. However, in many situations agents do care about how they are ranked by their potential matches. Thus, we allow an agent’s preference to depend on the preferences of the other side of the market and assume that agents “like to be liked”. We set up a simple model to explain how reciprocating preferences can rationally emerge and investigate how the standard deferred-acceptance mechanism (DA) performs when taking those preferences as given. While the DA is still strategy-proof for the proposing side, it loses stability. This is shown under two notions of stability. Next, we investigate whether a sequential variant of the DA that allows for information revelation before the mechanism takes place performs better. We define a two-stage deferred-acceptance mechanism (TSDA) in which one side of the market publicly announces their preferences before the other side submits their preferences to the mechanism. The TSDA can improve stability, but truth-telling is not a weakly dominant strategy for the proposing side anymore.