Incentives in Large Random Two-Sided Markets

Many centralized two-sided markets form a matching between participants by running a stable matching algorithm. It is a well-known fact that no matching mechanism based on a stable matching algorithm can guarantee truthfulness as a dominant strategy for participants. However, we show that in a probabilistic setting where the preference lists on one side of the market are composed of only a constant (independent of the size of the market) number of entries, each drawn from an arbitrary distribution, the number of participants that have more than one stable partner is vanishingly small. This proves (and generalizes) a conjecture of Roth and Peranson [1999]. As a corollary of this result, we show that, with high probability, the truthful strategy is the best response for a random player when the other players are truthful. We also analyze equilibria of the deferred acceptance stable matching game. We show that the game with complete information has an equilibrium in which, in expectation, a (1−o(1)) fraction of the strategies are truthful. In the more realistic setting of a game of incomplete information, we will show that the set of truthful stratiegs form a (1+o(1))-approximate Bayesian-Nash equilibrium for uniformly random preferences. Our results have implications in many practical settings and are inspired by the work of Roth and Peranson [1999] on the National Residency Matching Program.