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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 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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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

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Related research
Keywords: Equilibrim 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
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Matsuyama, Kiminori, 1992. "A Simple Model of Sectoral Adjustment," Review of Economic Studies, Blackwell Publishing, vol. 59(2), pages 375-88, April. [Downloadable!] (restricted)
  2. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November. [Downloadable!] (restricted)
  3. Fudenberg, D. & Harris, C., 1992. "Evolutionary dynamics with aggregate shocks," Journal of Economic Theory, Elsevier, vol. 57(2), pages 420-441, August. [Downloadable!] (restricted)
    Other versions:
  4. Joseph Farrell & Garth Saloner, 1985. "Standardization, Compatibility, and Innovation," RAND Journal of Economics, The RAND Corporation, vol. 16(1), pages 70-83, Spring. [Downloadable!] (restricted)
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  5. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-45, September. [Downloadable!] (restricted)
    Other versions:
  6. 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, January.
  7. Carlsson, H. & Van Damme, E., 1989. "Global Payoff Uncertainty And Risk Dominance," Papers 8933, Tilburg - Center for Economic Research.
  8. 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.
  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. [Downloadable!] (restricted)
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  10. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-71, September. [Downloadable!] (restricted)
  11. 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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  12. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May. [Downloadable!] (restricted)
  13. 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. [Downloadable!] (restricted)
  14. 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!]
  15. Swinkels Jeroen M., 1993. "Adjustment Dynamics and Rational Play in Games," Games and Economic Behavior, Elsevier, vol. 5(3), pages 455-484, July. [Downloadable!] (restricted)
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  16. 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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  17. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January. [Downloadable!] (restricted)
  18. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August. [Downloadable!] (restricted)
  19. Matsuyama, Kiminori, 1991. "Increasing Returns, Industrialization, and Indeterminacy of Equilibrium," The Quarterly Journal of Economics, MIT Press, vol. 106(2), pages 617-50, May. [Downloadable!] (restricted)
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  20. 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!]
  21. 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)
  22. Matsui, Akihiko, 1991. "Cheap-talk and cooperation in a society," Journal of Economic Theory, Elsevier, vol. 54(2), pages 245-258, August. [Downloadable!] (restricted)
  23. 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. [Downloadable!] (restricted)
  24. 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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  25. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September. [Downloadable!] (restricted)
  26. 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!]
  27. 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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  28. Boylan, Richard., 1990. "Equilibria Resistant to Mutation," Working Papers 729, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  29. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-67, May. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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:
  2. V. Bhaskar & George J. Mailath & Stephen Morris, 2009. "A Foundation for Markov Equilibria in Infinite Horizon Perfect Information Games," PIER Working Paper Archive 09-029, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania. [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!]
    Other versions:
  4. Shirley HO, 2004. "Evolutionary Forces in a Banking System with Speculation and System Risk," Econometric Society 2004 Far Eastern Meetings 692, Econometric Society. [Downloadable!]
  5. Angelo Antoci & Antonio Gay & Massimiliano Landi & Pier Luigi Sacco, 2007. "Global Analysis of an Expectations Augmented Evolutionary Dynamics," Working Papers 25-2007, Singapore Management University, School of Economics. [Downloadable!]
    Other versions:
  6. 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!]
    Other versions:
  7. 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!]
    Other versions:
  8. 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)
    Other versions:
  9. repec:att:wimass:19199923 is not listed on IDEAS
  10. Akihiko Matsui & Daisuke Oyama, 2002. "Rationalizable Foresight Dynamics: Evolution and Rationalizability," Vienna Economics Papers 0302, University of Vienna, Department of Economics. [Downloadable!]
  11. Huberto Ennis & Todd Keister, 2001. "Optimal policy with probabilistic equilibrium selection," Working Paper 01-03, Federal Reserve Bank of Richmond. [Downloadable!]
  12. Fernando Vega Redondo, 1993. "Shaping Long-Run Expectations In Problems Of Coordination," Working Papers. Serie AD 1993-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
  13. Lawrence E. Blume, 2003. "Stigma and Social Control," Game Theory and Information 0312002, EconWPA. [Downloadable!]
    Other versions:
  14. Kiminori Matsuyama, 1999. "Playing Multiple Complementarity Games Simultaneously," Discussion Papers 1240, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  15. 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!]
  16. Oyama, Daisuke & Tercieux, Olivier, 2004. "Iterated Potential and Robustness of Equilibria," MPRA Paper 1599, University Library of Munich, Germany, revised 22 Jan 2009. [Downloadable!]
    Other versions:
  17. Huberto M. Ennis, 2003. "Economic fundamentals and bank runs," Economic Quarterly, Federal Reserve Bank of Richmond, issue Spr, pages 55-71. [Downloadable!]
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