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An Approach to Equilibrium Selection

  • Akihiko Matsui
  • Kiminori Matsuyama

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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  1. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
  2. Gilboa, Itzhak & Matsui, Akihiko, 1992. "A model of random matching," Journal of Mathematical Economics, Elsevier, vol. 21(2), pages 185-197.
  3. Joseph Farrell & Garth Saloner, 1984. "Standardization, Compatibility and Innovation," Working papers 345, Massachusetts Institute of Technology (MIT), Department of Economics.
  4. Paul Krugman, 1990. "Increasing Returns and Economic Geography," NBER Working Papers 3275, National Bureau of Economic Research, Inc.
  5. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
  6. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  7. Kevin M. Murphy & Andrei Shleifer & Robert W. Vishny, 1988. "Industrialization and the Big Push," NBER Working Papers 2708, National Bureau of Economic Research, Inc.
  8. J. Swinkels, 2010. "Adjustment Dynamics and Rational Play in Games," Levine's Working Paper Archive 456, David K. Levine.
  9. Matsuyama, Kiminori, 1992. "A Simple Model of Sectoral Adjustment," Review of Economic Studies, Wiley Blackwell, vol. 59(2), pages 375-88, April.
  10. Itzhak Gilboa & Dov Samet, 1991. "Absorbent Stable Sets," Discussion Papers 935, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  11. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-67, May.
  12. Matsuyama, Kiminori, 1991. "Increasing Returns, Industrialization, and Indeterminacy of Equilibrium," The Quarterly Journal of Economics, MIT Press, vol. 106(2), pages 617-50, May.
  13. Ehud Kalai & Ehud Lehrer, 1990. "Rational Learning Leads to Nash Equilibrium," Discussion Papers 925, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  14. Judd, Kenneth L., 1985. "The law of large numbers with a continuum of IID random variables," Journal of Economic Theory, Elsevier, vol. 35(1), pages 19-25, February.
  15. Fudenberg, Drew & Harris, Christopher, 1992. "Evolutionary Dynamics with Aggregate Shocks," IDEI Working Papers 13, Institut d'Économie Industrielle (IDEI), Toulouse.
  16. Boylan, Richard T., 1992. "Laws of large numbers for dynamical systems with randomly matched individuals," Journal of Economic Theory, Elsevier, vol. 57(2), pages 473-504, August.
  17. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, August.
  18. repec:dgr:kubcen:198933 is not listed on IDEAS
  19. Carlsson, H. & van Damme, E.E.C., 1989. "Global payoff uncertainty and risk dominance," Discussion Paper 1989-33, Tilburg University, Center for Economic Research.
  20. 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.
  21. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September.
  22. 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.
  23. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  24. Glen Ellison, 2010. "Learning, Local Interaction, and Coordination," Levine's Working Paper Archive 391, David K. Levine.
  25. 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.
  26. Akihiko Matsui, 1989. "Cheap Talk and Cooperation in the Society," Discussion Papers 848, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  27. Douglas W. Diamond & Philip H. Dybvig, 2000. "Bank runs, deposit insurance, and liquidity," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Win, pages 14-23.
  28. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May.
  29. Matsui, Akihiko, 1991. "Cheap-talk and cooperation in a society," Journal of Economic Theory, Elsevier, vol. 54(2), pages 245-258, August.
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