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

  • Kiminori Matsuyama

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.

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File URL: http://www.kellogg.northwestern.edu/research/math/papers/940.pdf
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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 940.

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Date of creation: Jun 1991
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Handle: RePEc:nwu:cmsems:940
Contact details of provider: Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014
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Web page: http://www.kellogg.northwestern.edu/research/math/
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  1. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer, vol. 19(1), pages 59-89.
  2. Kiminori Matsuyama, 1990. "Increasing Returns, Industrialization and Indeterminacy of Equilibrium," Discussion Papers 878, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Gaertner, Wulf & Pattanaik, Prasanta K & Suzumura, Kotaro, 1992. "Individual Rights Revisited," Economica, London School of Economics and Political Science, vol. 59(234), pages 161-77, May.
  4. Karni, Edi & Schmeidler, David, 1990. "Fixed Preferences and Changing Tastes," American Economic Review, American Economic Association, vol. 80(2), pages 262-67, May.
  5. I. Gilboa & A. Matsui, 2010. "Social Stability and Equilibrium," Levine's Working Paper Archive 534, David K. Levine.
  6. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May.
  7. Sushil Bikhchandani & David Hirshleifer & Ivo Welch, 2010. "A theory of Fads, Fashion, Custom and cultural change as informational Cascades," Levine's Working Paper Archive 1193, David K. Levine.
  8. 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.
  9. Matsuyama, Kiminori, 1992. "A Simple Model of Sectoral Adjustment," Review of Economic Studies, Wiley Blackwell, vol. 59(2), pages 375-88, April.
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