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Anti-Coordination Games And Dynamic Stability

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Author Info

  • FUHITO KOJIMA

    ()
    (Department of Economics, Harvard University, 1805 Cambridge Street, Cambridge, MA 02138, USA)

  • SATORU TAKAHASHI

    ()
    (Department of Economics, Fisher Hall, 201 Princeton University, Princeton, NJ 08544, USA)

Abstract

We introduce the class of anti-coordination games. A symmetric two-player game is said to have the anti-coordination property if, for any mixed strategy, any worst response to the mixed strategy is in the support of the mixed strategy. Every anti-coordination game has a unique symmetric Nash equilibrium, which lies in the interior of the set of mixed strategies. We investigate the dynamic stability of the equilibrium in a one-population setting. Specifically we focus on the best response dynamic (BRD), where agents in a large population take myopic best responses, and the perfect foresight dynamic (PFD), where agents maximize total discounted payoffs from the present to the future. For any anti-coordination game we show (i) that, for any initial distribution, BRD has a unique solution, which reaches the equilibrium in a finite time, (ii) that the same path is one of the solutions to PFD, and (iii) that no path escapes from the equilibrium in PFD once the path reaches the equilibrium. Moreover we show (iv) that, in some subclasses of anti-coordination games, for any initial state, any solution to PFD converges to the equilibrium. All the results for PFD hold for any discount rate.

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Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Game Theory Review.

Volume (Year): 09 (2007)
Issue (Month): 04 ()
Pages: 667-688

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Handle: RePEc:wsi:igtrxx:v:09:y:2007:i:04:p:667-688

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Related research

Keywords: Anti-coordination games; best response dynamic; perfect foresight dynamic;

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Cited by:
  1. Daisuke Oyama & Satoru Takahashi & Josef Hofbauer, 2011. "Perfect foresight dynamics in binary supermodular games," International Journal of Economic Theory, The International Society for Economic Theory, vol. 7(3), pages 251-267, 09.
  2. Willemien Kets, 2007. "The minority game: An economics perspective," Science & Finance (CFM) working paper archive 0706.4432, Science & Finance, Capital Fund Management.
  3. Kets, W. & Voorneveld, M., 2007. "Congestion, Equilibrium and Learning: The Minority Game," Discussion Paper 2007-61, Tilburg University, Center for Economic Research.
  4. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2012. "Perturbations of Set-Valued Dynamical Systems, with Applications to Game Theory," Dynamic Games and Applications, Springer, vol. 2(2), pages 195-205, June.

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