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An Approach to Equilibrium Selection

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Author Info
Akihiko Matsui
Kiminori Matsuyama

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Abstract

We consider equilibrium selection in 2x2 bimatrix (both symmetric and asymmetric) games with two strict Nash equilibria by embedding it in a dynamic random matching game played by a continuum of anonymous agents. Unlike in the evolutionary game literature, we assume that the players are rational, seeking to maximize the expected discounted payoffs; but they are instead restricted to make a short run commitment when choosing actions. Modeling the friction this way yields the equilibrium dynamics, whose stationary states correspond to the Nash outcomes of the original game. Our selection is based on differential stability properties of the stationary states. It is shown that, as friction becomes arbitrarily small, a strict Nash outcome becomes uniquely absorbing and globally accessible if and only if it satisfies the Harsanyi and Selton (1988) notion of risk-dominance criterion. Our approach thus supplies another support for risk-dominance in addition to those given in literature.

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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 1065.

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Date of creation: Nov 1991
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Handle: RePEc:nwu:cmsems:1065

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Related research
Keywords: Equilibrium Selection Random Matching Games Risk-dominance

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

References listed on IDEAS
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  5. Carlsson, H. & Van Damme, E., 1989. "Global Payoff Uncertainty And Risk Dominance," Papers 8933, Tilburg - Center for Economic Research.
  6. David Canning, 1989. "Convergence to Equilibrium in a Sequence for Games with Learning," STICERD - Theoretical Economics Paper Series 190, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
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  9. Murphy, Kevin M & Shleifer, Andrei & Vishny, Robert W, 1989. "Industrialization and the Big Push," Journal of Political Economy, University of Chicago Press, vol. 97(5), pages 1003-26, October. [Downloadable!] (restricted)
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  10. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May. [Downloadable!] (restricted)
  11. Boylan, Richard T., 1990. "Laws of Large Numbers for Dynamical Systems with Randomly Matched Individuals," Working Papers 748, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
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  13. Kalai, Ehud & Lehrer, Ehud, 1991. "Rational Learning Leads to Nash Equilibrium," Working Papers 91-18, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
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  14. Diamond, Douglas W & Dybvig, Philip H, 1983. "Bank Runs, Deposit Insurance, and Liquidity," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 401-19, June. [Downloadable!] (restricted)
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  15. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January. [Downloadable!] (restricted)
  16. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August. [Downloadable!] (restricted)
  17. Akihiko Matsui, 1989. "Cheap Talk and Cooperation in the Society," Discussion Papers 848, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  18. Matsui, Akihiko, 1991. "Cheap-talk and cooperation in a society," Journal of Economic Theory, Elsevier, vol. 54(2), pages 245-258, August. [Downloadable!] (restricted)
  19. Cooper, Russell & John, Andrew, 1988. "Coordinating Coordination Failures in Keynesian Models," The Quarterly Journal of Economics, MIT Press, vol. 103(3), pages 441-63, August. [Downloadable!] (restricted)
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  21. Itzhak Gilboa & Akihiko Matsui, 1990. "A Model of Random Matching," Discussion Papers 887, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  22. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September. [Downloadable!] (restricted)
  23. 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. [Downloadable!]
  24. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-99, June. [Downloadable!] (restricted)
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  25. Boylan, Richard., 1990. "Equilibria Resistant to Mutation," Working Papers 729, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  26. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-67, May. [Downloadable!] (restricted)
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  1. repec:att:wimass:19199923 is not listed on IDEAS
  2. Daisuke Oyama & Satoru Takahashi & Josef Hofbauer, 2003. "Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics," Levine's Bibliography 666156000000000420, UCLA Department of Economics. [Downloadable!]
    Other versions:
  3. Stephen Morris & Hyun Song Shin, 2000. "Global Games: Theory and Applications," Cowles Foundation Discussion Papers 1275R, Cowles Foundation, Yale University, revised Aug 2001. [Downloadable!]
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  4. Akihiko Matsui & Daisuke Oyama, 2002. "Rationalizable Foresight Dynamics: Evolution and Rationalizability," Vienna Economics Papers 0302, University of Vienna, Department of Economics. [Downloadable!]
  5. Huberto Ennis & Todd Keister, 2001. "Optimal policy with probabilistic equilibrium selection," Working Paper 01-03, Federal Reserve Bank of Richmond. [Downloadable!]
  6. Lawrence E. Blume, 2003. "Stigma and Social Control," Game Theory and Information 0312002, EconWPA. [Downloadable!]
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  7. Kiminori Matsuyama, 1999. "Playing Multiple Complementarity Games Simultaneously," Discussion Papers 1240, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  8. Angelo Antoci & Massimiliano Landi & Pier Luigi Sacco, 2006. "Expectations, Animal Spirits, and Evolutionary Dynamics," Working Papers 10-2006, Singapore Management University, School of Economics. [Downloadable!]
  9. Shirley HO, 2004. "Evolutionary Forces in a Banking System with Speculation and System Risk," Econometric Society 2004 Far Eastern Meetings 692, Econometric Society. [Downloadable!]
  10. Oyama, Daisuke & Tercieux, Olivier, 2004. "Iterated Potential and Robustness of Equilibria," MPRA Paper 1599, University Library of Munich, Germany. [Downloadable!]
  11. David M. Frankel & Stephen Morris & Ady Pauzner, 2001. "Equilibrium Selection in Global Games with Strategic Complementarities," Cowles Foundation Discussion Papers 1336, Cowles Foundation, Yale University. [Downloadable!]
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  12. Huberto M. Ennis, 2003. "Economic fundamentals and bank runs," Economic Quarterly, Federal Reserve Bank of Richmond, issue Spr, pages 55-71. [Downloadable!]
  13. Carlos Alós-Ferrer, 1998. "- Dynamical Systems With A Continuum Of Randomly Matched Agents," Working Papers. Serie AD 1998-08, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
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  14. Kiminori Matsuyama, 1996. "Why Are There Rich and Poor Countries?: Symmetry-Breaking in the World Economy," NBER Working Papers 5697, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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