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An Approach to Equilibrium Selection

  • Akihiko Matsui
  • Kiminori Matsuyama

We consider equilibrium selection in 2x2 bimatrix games with two strict Nash equilibria in a random matching framework. The players seek to maximize the discounted payoffs, but are restricted to make a short run commitment. Modeling the friction this way yields equilibrium dynamics of the behavior patters in the society. We define and characterize an absorbing and globally attractive state in this dynamics. It is shown that, as friction becomes arbitrarily small, a strict Nash equilibrium outcome becomes unique absorbing and globally attractive if and only if it satisfies the Harsanyi/Selton notion of risk-dominance criterion.

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File URL: http://www.kellogg.northwestern.edu/research/math/papers/970.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 970.

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Date of creation: Nov 1990
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Handle: RePEc:nwu:cmsems:970
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. Akihiko Matsui, 1989. "Cheap Talk and Cooperation in the Society," Discussion Papers 848, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Paul Krugman, 1990. "Increasing Returns and Economic Geography," NBER Working Papers 3275, National Bureau of Economic Research, Inc.
  3. E. Kalai & E. Lehrer, 2010. "Rational Learning Leads to Nash Equilibrium," Levine's Working Paper Archive 529, David K. Levine.
  4. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  5. 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.
  6. Carlsson, H. & van Damme, E.E.C., 1989. "Global payoff uncertainty and risk dominance," Discussion Paper 1989-33, Tilburg University, Center for Economic Research.
  7. Itzhak Gilboa & Dov Samet, 1991. "Absorbent Stable Sets," Discussion Papers 935, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. KOHLBERG, Elon & MERTENS, Jean-François, . "On the strategic stability of equilibria," CORE Discussion Papers RP -716, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
  10. Fudenberg, Drew & Harris, Christopher, 1992. "Evolutionary Dynamics with Aggregate Shocks," IDEI Working Papers 13, Institut d'Économie Industrielle (IDEI), Toulouse.
  11. Matsuyama, Kiminori, 1991. "Increasing Returns, Industrialization, and Indeterminacy of Equilibrium," The Quarterly Journal of Economics, MIT Press, vol. 106(2), pages 617-50, May.
  12. 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.
  13. Gilboa, Itzhak & Matsui, Akihiko, 1992. "A model of random matching," Journal of Mathematical Economics, Elsevier, vol. 21(2), pages 185-197.
  14. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  15. J. Swinkels, 2010. "Adjustment Dynamics and Rational Play in Games," Levine's Working Paper Archive 456, David K. Levine.
  16. Matsui, Akihiko, 1991. "Cheap-talk and cooperation in a society," Journal of Economic Theory, Elsevier, vol. 54(2), pages 245-258, August.
  17. Murphy, Kevin M. & Shleifer, Andrei & Vishny, Robert W., 1989. "Industrialization and the Big Push," Scholarly Articles 3606235, Harvard University Department of Economics.
  18. 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.
  19. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
  20. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-71, September.
  21. Joseph Farrell & Garth Saloner, 1984. "Standardization, Compatibility and Innovation," Working papers 345, Massachusetts Institute of Technology (MIT), Department of Economics.
  22. 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, June.
  23. 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.
  24. repec:dgr:kubcen:198933 is not listed on IDEAS
  25. I. Gilboa & A. Matsui, 2010. "Social Stability and Equilibrium," Levine's Working Paper Archive 534, David K. Levine.
  26. Matsuyama, Kiminori, 1992. "A Simple Model of Sectoral Adjustment," Review of Economic Studies, Wiley Blackwell, vol. 59(2), pages 375-88, April.
  27. 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.
  28. 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.
  29. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May.
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