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

TL;DR

This paper explores the stability of matchings in marriage markets under evolving preference reports, using evolutionary game theory to demonstrate how stable outcomes can emerge through learning dynamics.

Contribution

It introduces the concept of asymptotic stability in preference revelation games and applies evolutionary dynamics to analyze stability in marriage problems.

Findings

Asymptotically stable matchings are stable when they exist.

Simulation of replicator dynamics confirms stability results.

Introducing a learning period can help achieve stable matchings.

Abstract

The literature on centralized matching markets often assumes that a true preference of each player is known to herself and fixed, but empirical evidence casts doubt on its plausibility. To circumvent the problem, we consider evolutionary dynamics of preference revelation games in marriage problems. We formulate the asymptotic stability of a matching, indicating the dynamical robustness against sufficiently small changes in players' preference reporting strategies, and show that asymptotically stable matchings are stable when they exist. The simulation results of replicator dynamics are presented to demonstrate the asymptotic stability. We contribute a practical insight for market designers that a stable matching may be realized by introducing a learning period in which participants find appropriate reporting strategies through trial and error. We also open doors to a novel area of research by demonstrating ways to employ evolutionary game theory in studies on centralized markets.