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Generalized Potentials and Robust Sets of Equilibria

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Author Info
Stephen Morris (Cowles Foundation, Yale University)
Takashi Ui (Yokohama National University)

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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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File URL: http://cowles.econ.yale.edu/P/cd/d13b/d1394.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1394.

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Length: 36 pages
Date of creation: Jan 2003
Date of revision:
Publication status: Published in Journal of Economic Theory (2005), 124: 45-78
Handle: RePEc:cwl:cwldpp:1394

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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Related research
Keywords: Incomplete information; Potential; Refinements; Robustness;

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information

This paper has been announced in the following NEP Reports:

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. Ui, Takashi, 2001. "Robust Equilibria of Potential Games," Econometrica, Econometric Society, vol. 69(5), pages 1373-80, September.
  2. Hofbauer, Josef & Sorger, Gerhard, 1999. "Perfect Foresight and Equilibrium Selection in Symmetric Potential Games," Journal of Economic Theory, Elsevier, vol. 85(1), pages 1-23, March. [Downloadable!] (restricted)
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  3. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
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  4. Kukushkin, Nikolai S., 1999. "Potential games: a purely ordinal approach," Economics Letters, Elsevier, vol. 64(3), pages 279-283, September. [Downloadable!] (restricted)
  5. Voorneveld, Mark, 2000. "Best-response potential games," Economics Letters, Elsevier, vol. 66(3), pages 289-295, March. [Downloadable!] (restricted)
  6. Ui, Takashi, 2000. "A Shapley Value Representation of Potential Games," Games and Economic Behavior, Elsevier, vol. 31(1), pages 121-135, April. [Downloadable!] (restricted)
  7. 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. [Downloadable!]
  8. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July. [Downloadable!] (restricted)
  9. Morris, Stephen Morris & Takashi Ui, 2002. "Best Response Equivalence," Cowles Foundation Discussion Papers 1377, Cowles Foundation, Yale University. [Downloadable!]
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  10. Carlsson, H. & Van Damme, E., 1990. "Global Games And Equilibrium Selection," Papers 9052, Tilburg - Center for Economic Research.
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  11. 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!]
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  12. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September. [Downloadable!] (restricted)
  13. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May. [Downloadable!] (restricted)
  14. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May. [Downloadable!] (restricted)
  15. Larry E. Blume, 1996. "Population Games," Working Papers 96-04-022, Santa Fe Institute.
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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 & Olivier Tercieux, 2007. "Robust Equilibria under Non-Common Priors," Levine's Bibliography 843644000000000210, UCLA Department of Economics. [Downloadable!]
    Other versions:
  2. Du, Songzi, 2008. "A Note on Intrinsic Correlation," MPRA Paper 12698, University Library of Munich, Germany, revised 12 Jan 2009. [Downloadable!]
  3. Oyama, Daisuke & Takahashi, Satoru & Hofbauer, Josef, 2003. "Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics," MPRA Paper 1555, University Library of Munich, Germany. [Downloadable!]
    Other versions:
  4. 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:
  5. 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:
  6. Hiroshi Uno, 2007. "Nested Potential Games," Economics Bulletin, Economics Bulletin, vol. 3(19), pages 1-8. [Downloadable!]
  7. Jonathan Weinstein & Muhamet Yildiz, 2004. "Finite-Order Implications of Any Equilibrium," Levine's Working Paper Archive 122247000000000065, David K. Levine. [Downloadable!]
  8. Daijiro Okada & Olivier Tercieux, 2008. "Log-linear Dynamics and Local Potential," Economics Working Papers 0085, Institute for Advanced Study, School of Social Science. [Downloadable!]
  9. Morris, Stephen Morris & Takashi Ui, 2002. "Best Response Equivalence," Cowles Foundation Discussion Papers 1377, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  10. Bernardo Guimaraes & Stephen Morris, 2003. "Risk and Wealth in a Model of Self-fulfilling Currency Crises," Cowles Foundation Discussion Papers 1433, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
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