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Incomplete Information Games with Multiple Priors

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  • Atsushi Kajii

    (Institute of Economic Research, Kyoto University)

  • Takashi Ui

    (Faculty of Economics, Yokohama National University)

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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Bibliographic 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
Date of revision:
Handle: RePEc:kyo:wpaper:583

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

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References

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  1. Kin Chung Lo, 1998. "Sealed bid auctions with uncertainty averse bidders," Economic Theory, Springer, vol. 12(1), pages 1-20.
  2. Mukerji, S. & Song Shin, H., 1997. "Equilibrium Departures From Common Knowledge in Games With Non-Additive Expected Utility," Economics Papers 137, Economics Group, Nuffield College, University of Oxford.
  3. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
  4. Stephen Morris & Hyun Song Shin, 2000. "Global Games: Theory and Applications," Cowles Foundation Discussion Papers 1275R, Cowles Foundation for Research in Economics, Yale University, revised Aug 2001.
  5. Epstein, Larry G & Zhang, Jiankang, 2001. "Subjective Probabilities on Subjectively Unambiguous Events," Econometrica, Econometric Society, vol. 69(2), pages 265-306, March.
  6. Harsanyi, John C, 1995. "Games with Incomplete Information," American Economic Review, American Economic Association, vol. 85(3), pages 291-303, June.
  7. Paul Milgrom & Nancy L.Stokey, 1979. "Information, Trade, and Common Knowledge," Discussion Papers 377R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Dow, James & Werlang, Sérgio Ribeiro da Costa, 1992. "Nash equilibrium under knightian uncertainty: breaking-down backward induction," Economics Working Papers (Ensaios Economicos da EPGE) 186, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  9. Lo, Kin Chung, 1996. "Equilibrium in Beliefs under Uncertainty," Journal of Economic Theory, Elsevier, vol. 71(2), pages 443-484, November.
  10. Crawford, Vincent P., 1990. "Equilibrium without independence," Journal of Economic Theory, Elsevier, vol. 50(1), pages 127-154, February.
  11. Epstein, L.G. & Zhang, J., 1998. "Subjective Probabilities on Subjectivity Unambiguous Event," RCER Working Papers 456, University of Rochester - Center for Economic Research (RCER).
  12. Morris, Stephen & Shin, Hyun Song, 1997. "Unique Equilibrium in a Model of Self-fulfilling Currency Attacks," CEPR Discussion Papers 1687, C.E.P.R. Discussion Papers.
  13. Epstein, Larry G & Wang, Tan, 1996. ""Beliefs about Beliefs" without Probabilities," Econometrica, Econometric Society, vol. 64(6), pages 1343-73, November.
  14. Atsushi Kajii & Takashi Ui, 2004. "Trade with Heterogeneous Multiple Priors," KIER Working Papers 582, Kyoto University, Institute of Economic Research.
  15. Lo, Kin Chung, 2002. "Correlated equilibrium under uncertainty," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 183-209, November.
  16. Robert J Aumann, 1999. "Agreeing to Disagree," Levine's Working Paper Archive 512, David K. Levine.
  17. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  18. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
  19. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  20. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February.
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Citations

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Cited by:
  1. Giuseppe De Marco & Maria Romaniello, 2011. "A Limit Theorem for Equilibria under Ambiguous Beliefs Correspondences," CSEF Working Papers 299, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
  2. Atsushi Kajii & Takashi Ui, 2004. "Trade with Heterogeneous Multiple Priors," KIER Working Papers 582, Kyoto University, Institute of Economic Research.
  3. Aryal, Gaurab & Stauber, Ronald, 2014. "A Note on Kuhn’s Theorem with Ambiguity Averse Players," MPRA Paper 57336, University Library of Munich, Germany.
  4. : Kostas Koufopoulos & : Roman Kozhan, 2012. "Optimal Insurance under Advserse Selection and Ambiguity Aversion," Working Papers wpn12-07, Warwick Business School, Finance Group.
  5. Kajii, Atsushi & Ui, Takashi, 2009. "Interim efficient allocations under uncertainty," Journal of Economic Theory, Elsevier, vol. 144(1), pages 337-353, January.
  6. Stauber, Ronald, 2011. "Knightian games and robustness to ambiguity," Journal of Economic Theory, Elsevier, vol. 146(1), pages 248-274, January.
  7. Gaurab Aryal & Ronald Stauber, 2013. "Trembles in Extensive Games with Ambiguity Averse Players," ANU Working Papers in Economics and Econometrics 2013-606, Australian National University, College of Business and Economics, School of Economics.
  8. Azrieli, Yaron & Teper, Roee, 2011. "Uncertainty aversion and equilibrium existence in games with incomplete information," Games and Economic Behavior, Elsevier, vol. 73(2), pages 310-317.
  9. Ronald Stauber, 2014. "A framework for robustness to ambiguity of higher-order beliefs," International Journal of Game Theory, Springer, vol. 43(3), pages 525-550, August.
  10. Ronald Stauber, 2013. "A Framework for Robustness to Ambiguity of Higher-Order Beliefs," ANU Working Papers in Economics and Econometrics 2013-602, Australian National University, College of Business and Economics, School of Economics.

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