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Custom Versus Fashion: Hysteresis and Limit Cycles in a Random Matching Game

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  • Kiminori Matsuyama

Abstract

This paper considers a simple pairwise random matching game in the society populated by two groups of agents: Conformists and Nonconformists. Depending on the relative frequencies of intergroup and intragroup matchings, the best response dynamics show three types of asymptotic behaviors: global convergence, hysteresis and limit cycles. In the hysteresis case, Conformists set the social custom, and Nonconformists revolt against it; what action becomes the custom is determined by "history." In the limit cycle case, Nonconformists become fashion leaders and switch their actions periodically, while Conformists follow with delay.

Suggested Citation

  • Kiminori Matsuyama, 1991. "Custom Versus Fashion: Hysteresis and Limit Cycles in a Random Matching Game," Discussion Papers 940, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:940
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    References listed on IDEAS

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    1. Kiminori Matsuyama, 1991. "Increasing Returns, Industrialization, and Indeterminacy of Equilibrium," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(2), pages 617-650.
    2. Karni, Edi & Schmeidler, David, 1990. "Fixed Preferences and Changing Tastes," American Economic Review, American Economic Association, vol. 80(2), pages 262-267, May.
    3. repec:bla:econom:v:59:y:1992:i:234:p:161-77 is not listed on IDEAS
    4. Bulow, Jeremy I & Geanakoplos, John D & Klemperer, Paul D, 1985. "Multimarket Oligopoly: Strategic Substitutes and Complements," Journal of Political Economy, University of Chicago Press, vol. 93(3), pages 488-511, June.
    5. Bikhchandani, Sushil & Hirshleifer, David & Welch, Ivo, 1992. "A Theory of Fads, Fashion, Custom, and Cultural Change in Informational Cascades," Journal of Political Economy, University of Chicago Press, vol. 100(5), pages 992-1026, October.
    6. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-867, May.
    7. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-666, May.
    8. Kiminori Matsuyama & Nobuhiro Kiyotaki & Akihiko Matsui, 1993. "Toward a Theory of International Currency," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(2), pages 283-307.
    9. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(1), pages 59-89.
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    Cited by:

    1. Matsui Akihiko & Matsuyama Kiminori, 1995. "An Approach to Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 65(2), pages 415-434, April.
    2. Bernheim, B Douglas, 1994. "A Theory of Conformity," Journal of Political Economy, University of Chicago Press, vol. 102(5), pages 841-877, October.
    3. Karni, Edi & Levin, Dan, 1994. "Social Attributes and Strategic Equilibrium: A Restaurant Pricing Game," Journal of Political Economy, University of Chicago Press, vol. 102(4), pages 822-840, August.
    4. Bikhchandani, Sushil & Hirshleifer, David & Welch, Ivo, 1992. "A Theory of Fads, Fashion, Custom, and Cultural Change in Informational Cascades," Journal of Political Economy, University of Chicago Press, vol. 100(5), pages 992-1026, October.
    5. Baumann, Leonie & Olszewski, Wojciech, 2021. "Demand cycles and heterogeneous conformity preferences," Journal of Economic Theory, Elsevier, vol. 194(C).
    6. Cabo, Francisco & García-González, Ana, 2020. "Interaction and imitation with heterogeneous agents: A misleading evolutionary equilibrium," Journal of Economic Behavior & Organization, Elsevier, vol. 179(C), pages 152-174.
    7. Agnès Festré, 2010. "Incentives And Social Norms: A Motivation‐Based Economic Analysis Of Social Norms," Journal of Economic Surveys, Wiley Blackwell, vol. 24(3), pages 511-538, July.

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