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The literature on centralized matching markets often assumes that a truepreference of each player is known to herself and fixed, but empirical evidencecasts doubt on its plausibility. To circumvent the problem, we considerevolutionary dynamics of preference revelation games in marriage problems. Weformulate the asymptotic stability of a matching, indicating the dynamicalrobustness against sufficiently small changes in players' preference reportingstrategies, and show that asymptotically stable matchings are stable when theyexist. The simulation results of replicator dynamics are presented todemonstrate the asymptotic stability. We contribute a practical insight formarket designers that a stable matching may be realized by introducing alearning period in which participants find appropriate reporting strategiesthrough trial and error. We also open doors to a novel area of research bydemonstrating ways to employ evolutionary game theory in studies on centralizedmarkets.

Asymptotically stable matchings and evolutionary dynamics of preference revelation games in marriage problems