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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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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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  1. Atsushi Kajii & Stephen Morris, 1997. "Refinements and Social Order Beliefs: A Unified Survey," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1197, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Lawrence Blume, 1996. "Population Games," Game Theory and Information, EconWPA 9607001, EconWPA.
  3. L. Blume, 2010. "The Statistical Mechanics of Strategic Interaction," Levine's Working Paper Archive 488, David K. Levine.
  4. Carlsson, H. & Damme, E.E.C. van, 1993. "Global games and equilibrium selection," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154416, Tilburg University.
  5. KOHLBERG, Elon & MERTENS, Jean-François, . "On the strategic stability of equilibria," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -716, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Frankel, David M. & Morris, Stephen & Pauzner, Ady, 2003. "Equilibrium selection in global games with strategic complementarities," Journal of Economic Theory, Elsevier, Elsevier, vol. 108(1), pages 1-44, January.
  7. Akihiko Matsui & Kiminori Matsuyama, 1991. "An Approach to Equilibrium Selection," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1065, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Oyama, Daisuke, 2002. "p-Dominance and Equilibrium Selection under Perfect Foresight Dynamics," Journal of Economic Theory, Elsevier, Elsevier, vol. 107(2), pages 288-310, December.
  9. Morris, Stephen & Ui, Takashi, 2004. "Best response equivalence," Games and Economic Behavior, Elsevier, Elsevier, vol. 49(2), pages 260-287, November.
  10. Gerhard SORGER, 1998. "Perfect Foresight and Equilibrium Selection in Symmetric Potential Games," Vienna Economics Papers, University of Vienna, Department of Economics 9802, University of Vienna, Department of Economics.
  11. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, Elsevier, vol. 14(1), pages 124-143, May.
  12. Atsushi Kajii & Stephen Morris, . "The Robustness of Equilibria to Incomplete Information," Penn CARESS Working Papers, Penn Economics Department ed504c985fc375cbe719b3f60, Penn Economics Department.
  13. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, Econometric Society, vol. 57(3), pages 589-614, May.
  14. Ui, Takashi, 2001. "Robust Equilibria of Potential Games," Econometrica, Econometric Society, Econometric Society, vol. 69(5), pages 1373-80, September.
  15. Toshimasa Maruta, 1995. "On the Relationship Between Risk-Dominance and Stochastic Stability," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1122, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  16. Kukushkin, Nikolai S., 1999. "Potential games: a purely ordinal approach," Economics Letters, Elsevier, Elsevier, vol. 64(3), pages 279-283, September.
  17. Ui, Takashi, 2000. "A Shapley Value Representation of Potential Games," Games and Economic Behavior, Elsevier, Elsevier, vol. 31(1), pages 121-135, April.
  18. Ellison, Glenn, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 67(1), pages 17-45, January.
  19. Voorneveld, Mark, 2000. "Best-response potential games," Economics Letters, Elsevier, Elsevier, vol. 66(3), pages 289-295, March.
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