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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.

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Bibliographic Info

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

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Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014
Phone: 847/491-3527
Fax: 847/491-2530
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Web page: http://www.kellogg.northwestern.edu/research/math/
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Keywords: Best response dynamics; Bifurcation; Equilibrium refinement; Evolutionary process; Hysteresis; Limit Cycles; Perfect foresight; dynamics; Strategic complements and substitutes.;

References

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  1. 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.
  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. Matsuyama, Kiminori, 1992. "A Simple Model of Sectoral Adjustment," Review of Economic Studies, Wiley Blackwell, vol. 59(2), pages 375-88, April.
  4. 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.
  5. I. Gilboa & A. Matsui, 2010. "Social Stability and Equilibrium," Levine's Working Paper Archive 534, David K. Levine.
  6. 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.
  7. Karni, Edi & Schmeidler, David, 1990. "Fixed Preferences and Changing Tastes," American Economic Review, American Economic Association, vol. 80(2), pages 262-67, May.
  8. 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.
  9. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May.
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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.

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