Strategic Behavior in Matching Markets

Centralized two-sided markets, such as the market for medical residents, often rely on a stable matching mechanism to determine a matching between participants. Because no stable matching mechanism can induce truth-telling as a dominant strategy for all participants, there is always some room in these markets for strategic misrepresentation. In this paper we study optimal strategic misrepresentation. Roth and Rothblum [9] find that in settings with a form of informational symmetry, submitting a truncated version of one’s true preference list must be optimal. We provide a framework which allows us to evaluate the consequences of truncation. We characterize the return to truncation for general beliefs, and solve for payoffs in a particular symmetric setting. We show that there is a unique optimal truncation point and use this result to prove the existence of a pure strategy truncation equilibrium. We then relax the symmetry requirement and show that the more risk averse a player, the lower the degree of her optimal truncation. Hence, more conservative players should be wary of trying to ‘game the system.’ As correlation in preferences increases, players should truncate less, implying that correlation too indicates less room for strategic misrepresentation.