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An Approach to Equilibrium Selection

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  • Akihiko Matsui
  • Kiminori Matsuyama

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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Bibliographic Info

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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Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014
Phone: 847/491-3527
Fax: 847/491-2530
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Web page: http://www.kellogg.northwestern.edu/research/math/
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Keywords: Equilibrim Selection; Random Matching Games; risk-dominance;

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References

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  1. Murphy, Kevin M. & Shleifer, Andrei & Vishny, Robert W., 1989. "Industrialization and the Big Push," Scholarly Articles 3606235, Harvard University Department of Economics.
  2. Carlsson, H. & Van Damme, E., 1989. "Global Payoff Uncertainty And Risk Dominance," Papers 8933, Tilburg - Center for Economic Research.
  3. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September.
  4. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-71, September.
  5. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-67, May.
  6. Jeroen M. Swinkels, 1991. "Adjustment Dynamics and Rational Play in Games," Discussion Papers 1001, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
  8. 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.
  9. Akihiko Matsui, 1989. "Cheap Talk and Cooperation in the Society," Discussion Papers 848, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. 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.
  11. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May.
  12. Fudenberg, D. & Harris, C., 1992. "Evolutionary dynamics with aggregate shocks," Journal of Economic Theory, Elsevier, vol. 57(2), pages 420-441, August.
  13. 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.
  14. Itzhak Gilboa & Dov Samet, 1991. "Absorbent Stable Sets," Discussion Papers 935, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  15. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  16. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
  17. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-99, June.
  18. 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, December.
  19. Matsuyama, Kiminori, 1992. "A Simple Model of Sectoral Adjustment," Review of Economic Studies, Wiley Blackwell, vol. 59(2), pages 375-88, April.
  20. Itzhak Gilboa & Akihiko Matsui, 1990. "A Model of Random Matching," Discussion Papers 887, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  21. Joseph Farrell & Garth Saloner, 1984. "Standardization, Compatibility and Innovation," Working papers 345, Massachusetts Institute of Technology (MIT), Department of Economics.
  22. Matsui, Akihiko, 1991. "Cheap-talk and cooperation in a society," Journal of Economic Theory, Elsevier, vol. 54(2), pages 245-258, August.
  23. 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.
  24. Kiminori Matsuyama, 1990. "Increasing Returns, Industrialization and Indeterminacy of Equilibrium," Discussion Papers 878, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  25. 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.
  26. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  27. 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.
  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.
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