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Incomplete Information Games with Multiple Priors

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Author Info
Atsushi Kajii (Institute of Economic Research, Kyoto University)
Takashi Ui (Faculty of Economics, Yokohama National University)

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Abstract

We present a model of incomplete information games with sets of priors. Upon arrival of private information, each player “updates” by the Bayes rule each of priors in this set to construct the set of posteriors consistent with the arrived piece of information. Then the player uses a possibly proper subset of this set of posteriors to form beliefs about the opponents’ strategic choices. And finally the player evaluates his actions by the most pessimistic posterior beliefs `a la Gilboa and Schmeidler (1989). So each player’s preferences may exhibit non-linearity in probabilities which can be interpreted as the player’s aversion to ambiguity or uncertainty. In this setup, we define a couple of equilibrium concepts, establish existence results for them, and demonstrate by examples how players’ views on uncertainty about the environment affect the strategic outcomes.

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Publisher Info
Paper provided by Kyoto University, Institute of Economic Research in its series KIER Working Papers with number 583.

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Length: 23 pages
Date of creation: May 2004
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Handle: RePEc:kyo:wpaper:583

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Related research
Keywords: incomplete information games; multiple priors; ambiguity aversion; uncertainty aversion;

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information

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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. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February. [Downloadable!] (restricted)
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  2. Atsushi Kajii & Takashi Ui, 2004. "Trade with Heterogeneous Multiple Priors," KIER Working Papers 582, Kyoto University, Institute of Economic Research. [Downloadable!]
  3. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April. [Downloadable!] (restricted)
  4. repec:bep:theadv:v:2:y:2002:i:1:p:1011-1011 is not listed on IDEAS
  5. Crawford, Vincent P., 1990. "Equilibrium without independence," Journal of Economic Theory, Elsevier, vol. 50(1), pages 127-154, February. [Downloadable!] (restricted)
  6. Morris, Stephen & Shin, Hyun Song, 1998. "Unique Equilibrium in a Model of Self-Fulfilling Currency Attacks," American Economic Review, American Economic Association, vol. 88(3), pages 587-97, June. [Downloadable!] (restricted)
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  7. Stephen Morris & Hyun S Shin, 2001. "Global Games: Theory and Applications," Levine's Working Paper Archive 122247000000001080, David K. Levine. [Downloadable!]
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  8. Milgrom, Paul & Stokey, Nancy, 1982. "Information, trade and common knowledge," Journal of Economic Theory, Elsevier, vol. 26(1), pages 17-27, February. [Downloadable!] (restricted)
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  9. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February. [Downloadable!] (restricted)
  10. Harsanyi, John C, 1995. "Games with Incomplete Information," American Economic Review, American Economic Association, vol. 85(3), pages 291-303, June.
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  11. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May. [Downloadable!] (restricted)
  12. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September. [Downloadable!] (restricted)
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  13. Epstein, Larry G & Zhang, Jiankang, 2001. "Subjective Probabilities on Subjectively Unambiguous Events," Econometrica, Econometric Society, vol. 69(2), pages 265-306, March.
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  14. Epstein, Larry G & Wang, Tan, 1996. ""Beliefs about Beliefs" without Probabilities," Econometrica, Econometric Society, vol. 64(6), pages 1343-73, November. [Downloadable!] (restricted)
  15. Lo, Kin Chung, 1996. "Equilibrium in Beliefs under Uncertainty," Journal of Economic Theory, Elsevier, vol. 71(2), pages 443-484, November. [Downloadable!] (restricted)
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  16. Lo, Kin Chung, 2002. "Correlated equilibrium under uncertainty," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 183-209, November. [Downloadable!] (restricted)
  17. Dow James & Werlang Sergio Ribeiro Da Costa, 1994. "Nash Equilibrium under Knightian Uncertainty: Breaking Down Backward Induction," Journal of Economic Theory, Elsevier, vol. 64(2), pages 305-324, December. [Downloadable!] (restricted)
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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. Azrieli, Yaron & Teper, Roee, 2009. "Uncertainty aversion and equilibrium existence in games with incomplete information," MPRA Paper 17615, University Library of Munich, Germany. [Downloadable!]
  2. Atsushi Kajii & Takashi Ui, 2004. "Trade with Heterogeneous Multiple Priors," KIER Working Papers 582, Kyoto University, Institute of Economic Research. [Downloadable!]
  3. Atsushi Kajii & Takashi Ui, 2007. "Interim Efficient Allocations under Uncertainty," KIER Working Papers 642, Kyoto University, Institute of Economic Research. [Downloadable!]
    Other versions:
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