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Generalized Potentials and Robust Sets of Equilibria

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  • Stephen Morris
  • Takashi Ui

Abstract

This paper introduces generalized potential functions of complete information games and studies the robustness of sets of equilibria to incomplete information. A set of equilibria of a complete information game is robust if every incomplete information game where payoffs are almost always given by the complete information game has an equilibrium which generates behavior close to some equilibrium in the set. This paper provides sufficient conditions for the robustness of sets of equilibria in terms of argmax sets of generalized potential functions and shows that the sufficient conditions generalize the existing sufficient conditions for the robustness of equilibria.

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Bibliographic Info

Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 506439000000000325.

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Date of creation: 20 Feb 2003
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Handle: RePEc:cla:levarc:506439000000000325

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References

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  1. Hans Carlsson & Eric van Damme, 1993. "Global Games and Equilibrium Selection," Levine's Working Paper Archive 122247000000001088, David K. Levine.
  2. Matsui Akihiko & Matsuyama Kiminori, 1995. "An Approach to Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 65(2), pages 415-434, April.
  3. L. Blume, 2010. "The Statistical Mechanics of Strategic Interaction," Levine's Working Paper Archive 488, David K. Levine.
  4. Larry E. Blume, 1996. "Population Games," Working Papers 96-04-022, Santa Fe Institute.
  5. David M. Frankel & Stephen Morris & Ady Pauzner, 2000. "Equilibrium Selection in Global Games with Strategic Complementarities," Econometric Society World Congress 2000 Contributed Papers 1490, Econometric Society.
  6. Morris, Stephen & Ui, Takashi, 2004. "Best response equivalence," Games and Economic Behavior, Elsevier, vol. 49(2), pages 260-287, November.
  7. Ellison, Glenn, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," Review of Economic Studies, Wiley Blackwell, vol. 67(1), pages 17-45, January.
  8. Voorneveld, Mark, 2000. "Best-response potential games," Economics Letters, Elsevier, vol. 66(3), pages 289-295, March.
  9. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  10. Gerhard SORGER, 1998. "Perfect Foresight and Equilibrium Selection in Symmetric Potential Games," Vienna Economics Papers 9802, University of Vienna, Department of Economics.
  11. Atsushi Kajii & Stephen Morris, . ""The Robustness of Equilibria to Incomplete Information*''," CARESS Working Papres 95-18, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  12. Toshimasa Maruta, 1995. "On the Relationship Between Risk-Dominance and Stochastic Stability," Discussion Papers 1122, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  13. E. Kohlberg & J.-F. Mertens, 1998. "On the Strategic Stability of Equilibria," Levine's Working Paper Archive 445, David K. Levine.
  14. Ui, Takashi, 2000. "A Shapley Value Representation of Potential Games," Games and Economic Behavior, Elsevier, vol. 31(1), pages 121-135, April.
  15. Oyama, Daisuke, 2002. "p-Dominance and Equilibrium Selection under Perfect Foresight Dynamics," Journal of Economic Theory, Elsevier, vol. 107(2), pages 288-310, December.
  16. Ui, Takashi, 2001. "Robust Equilibria of Potential Games," Econometrica, Econometric Society, vol. 69(5), pages 1373-80, September.
  17. Atsushi Kajii & Stephen Morris, 1997. "Refinements and Social Order Beliefs: A Unified Survey," Discussion Papers 1197, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  18. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  19. Kukushkin, Nikolai S., 1999. "Potential games: a purely ordinal approach," Economics Letters, Elsevier, vol. 64(3), pages 279-283, September.
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