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Robust Equilibria under Non-Common Priors

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Author Info
Oyama, Daisuke
Tercieux, Olivier

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Abstract

This paper considers the robustness of equilibria to a small amount of incomplete information, where players are allowed to have heterogenous priors. An equilibrium of a complete information game is robust to incomplete information under non-common priors if for every incomplete information game where each player's prior assigns high probability on the event that the players know at arbitrarily high order that the payoffs are given by the complete information game, there exists a Bayesian Nash equilibrium that generates behavior close to the equilibrium in consideration. It is shown that for generic games, an equilibrium is robust under non-common priors if and only if it is the unique rationalizable action profile. Set-valued concepts are also introduced, and for generic games, a smallest robust set is shown to exist and coincide with the set of a posteriori equilibria.

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File URL: http://mpra.ub.uni-muenchen.de/7734/
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 7734.

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Date of creation: 31 Dec 2005
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Handle: RePEc:pra:mprapa:7734

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Related research
Keywords: incomplete information robustness common prior assumption higher order belief

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

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  1. Ui, Takashi, 2001. "Robust Equilibria of Potential Games," Econometrica, Econometric Society, vol. 69(5), pages 1373-80, September.
  2. Fudenberg, Drew & Kreps, David M. & Levine, David K., 1988. "On the robustness of equilibrium refinements," Journal of Economic Theory, Elsevier, vol. 44(2), pages 354-380, April. [Downloadable!] (restricted)
    Other versions:
  3. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
    Other versions:
  4. Dekel, Eddie & Fudenberg, Drew & Levine, David K., 2004. "Learning to play Bayesian games," Games and Economic Behavior, Elsevier, vol. 46(2), pages 282-303, February. [Downloadable!] (restricted)
    Other versions:
  5. Oyama, Daisuke & Tercieux, Olivier, 2005. "On the Strategic Impact of an Event under Non-Common Priors," MPRA Paper 4559, University Library of Munich, Germany. [Downloadable!]
  6. Oyama, Daisuke & Tercieux, Olivier, 2004. "Iterated Potential and Robustness of Equilibria," MPRA Paper 1599, University Library of Munich, Germany. [Downloadable!]
  7. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March. [Downloadable!] (restricted)
  8. Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2007. "Interim correlated rationalizability," Theoretical Economics, Society for Economic Theory, vol. 2(1), pages 15-40, March. [Downloadable!]
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  9. Barton L. Lipman, 2005. "Finite Order Implications of Common Priors in Infinite Models," Boston University - Department of Economics - Working Papers Series WP2005-009, Boston University - Department of Economics. [Downloadable!]
  10. Jonathan Weinstein & Muhamet Yildiz, 2007. "A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements," Econometrica, Econometric Society, vol. 75(2), pages 365-400, 03. [Downloadable!] (restricted)
  11. Pierpaolo Battigalli & Marciano Siniscalchi, 2003. "Rationalization and Incomplete Information," Advances in Theoretical Economics, Berkeley Electronic Press, vol. 3(1), pages 1073-1073. [Downloadable!] (restricted)
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  12. Jonathan Weinstein & Muhamet Yildiz, 2004. "Finite-Order Implications of Any Equilibrium," Levine's Working Paper Archive 122247000000000065, UCLA Department of Economics. [Downloadable!]
  13. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June. [Downloadable!] (restricted)
  14. Morris, Stephen & Ui, Takashi, 2005. "Generalized potentials and robust sets of equilibria," Journal of Economic Theory, Elsevier, vol. 124(1), pages 45-78, September. [Downloadable!] (restricted)
    Other versions:
  15. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September. [Downloadable!] (restricted)
  16. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, vol. 55(6), pages 1391-1402, November. [Downloadable!] (restricted)
  17. Morris, Stephen & Rob, Rafael & Shin, Hyun Song, 1995. "Dominance and Belief Potential," Econometrica, Econometric Society, vol. 63(1), pages 145-57, January. [Downloadable!] (restricted)
  18. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February. [Downloadable!] (restricted)
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