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

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  • Hidemasa Ishii
  • Nariaki Nishino

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.

Suggested Citation

  • Hidemasa Ishii & Nariaki Nishino, 2022. "Asymptotically stable matchings and evolutionary dynamics of preference revelation games in marriage problems," Papers 2205.08079, arXiv.org.
    • Handle: RePEc:arx:papers:2205.08079
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    References listed on IDEAS

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    1. Alcalde, Jose, 1996. "Implementation of Stable Solutions to Marriage Problems," Journal of Economic Theory, Elsevier, vol. 69(1), pages 240-254, April.
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    3. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, April.
    4. Bilancini, Ennio & Boncinelli, Leonardo & Newton, Jonathan, 2020. "Evolution and Rawlsian social choice in matching," Games and Economic Behavior, Elsevier, vol. 123(C), pages 68-80.
    5. Ma Jinpeng, 1995. "Stable Matchings and Rematching-Proof Equilibria in a Two-Sided Matching Market," Journal of Economic Theory, Elsevier, vol. 66(2), pages 352-369, August.
    6. repec:hhs:iuiwop:487 is not listed on IDEAS
    7. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-1480, November.
    8. Fuhito Kojima & Parag A. Pathak, 2009. "Incentives and Stability in Large Two-Sided Matching Markets," American Economic Review, American Economic Association, vol. 99(3), pages 608-627, June.
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