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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. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  2. Crawford, Vincent P., 1990. "Equilibrium without independence," Journal of Economic Theory, Elsevier, Elsevier, vol. 50(1), pages 127-154, February.
  3. Mukerji Sujoy & Shin Hyun Song, 2002. "Equilibrium Departures from Common Knowledge in Games with Non-Additive Expected Utility," The B.E. Journal of Theoretical Economics, De Gruyter, De Gruyter, vol. 2(1), pages 1-30, June.
  4. Kin Chung Lo, 1998. "Sealed bid auctions with uncertainty averse bidders," Economic Theory, Springer, Springer, vol. 12(1), pages 1-20.
  5. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  6. Epstein, Larry G & Zhang, Jiankang, 2001. "Subjective Probabilities on Subjectively Unambiguous Events," Econometrica, Econometric Society, Econometric Society, vol. 69(2), pages 265-306, March.
  7. Stephen Morris & Hyun Song Shin, 2000. "Global Games: Theory and Applications," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1275R, Cowles Foundation for Research in Economics, Yale University, revised Aug 2001.
  8. Atsushi Kajii & Takashi Ui, 2004. "Trade with Heterogeneous Multiple Priors," KIER Working Papers, Kyoto University, Institute of Economic Research 582, Kyoto University, Institute of Economic Research.
  9. 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).
  10. Lo, Kin Chung, 1996. "Equilibrium in Beliefs under Uncertainty," Journal of Economic Theory, Elsevier, Elsevier, vol. 71(2), pages 443-484, November.
  11. Carlsson, H. & Van Damme, E., 1990. "Global Games And Equilibrium Selection," Papers, Tilburg - Center for Economic Research 9052, Tilburg - Center for Economic Research.
  12. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, Elsevier, vol. 59(1), pages 33-49, February.
  13. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, Elsevier, vol. 30(2), pages 183-215, February.
  14. Epstein, Larry G & Wang, Tan, 1996. ""Beliefs about Beliefs" without Probabilities," Econometrica, Econometric Society, Econometric Society, vol. 64(6), pages 1343-73, November.
  15. Milgrom, Paul & Stokey, Nancy, 1982. "Information, trade and common knowledge," Journal of Economic Theory, Elsevier, Elsevier, vol. 26(1), pages 17-27, February.
  16. Lo, Kin Chung, 2002. "Correlated equilibrium under uncertainty," Mathematical Social Sciences, Elsevier, Elsevier, vol. 44(2), pages 183-209, November.
  17. Morris, Stephen & Shin, Hyun Song, 1998. "Unique Equilibrium in a Model of Self-Fulfilling Currency Attacks," American Economic Review, American Economic Association, American Economic Association, vol. 88(3), pages 587-97, June.
  18. Robert J Aumann, 1999. "Agreeing to Disagree," Levine's Working Paper Archive 512, David K. Levine.
  19. Harsanyi, John C., 1994. "Games with Incomplete Information," Nobel Prize in Economics documents, Nobel Prize Committee 1994-1, Nobel Prize Committee.
  20. Epstein, L.G. & Zhang, J., 1998. "Subjective Probabilities on Subjectivity Unambiguous Event," RCER Working Papers 456, University of Rochester - Center for Economic Research (RCER).
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Citations

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Cited by:
  1. Ronald Stauber, 2013. "A Framework for Robustness to Ambiguity of Higher-Order Beliefs," ANU Working Papers in Economics and Econometrics, Australian National University, College of Business and Economics, School of Economics 2013-602, Australian National University, College of Business and Economics, School of Economics.
  2. Aryal, Gaurab & Stauber, Ronald, 2014. "A Note on Kuhn’s Theorem with Ambiguity Averse Players," MPRA Paper 57336, University Library of Munich, Germany.
  3. Atsushi Kajii & Takashi Ui, 2004. "Trade with Heterogeneous Multiple Priors," KIER Working Papers, Kyoto University, Institute of Economic Research 582, Kyoto University, Institute of Economic Research.
  4. Gaurab Aryal & Ronald Stauber, 2014. "A Note on Kuhn's Theorem with Ambiguity Averse Players," Papers 1408.1022, arXiv.org, revised Aug 2014.
  5. Stauber, Ronald, 2011. "Knightian games and robustness to ambiguity," Journal of Economic Theory, Elsevier, Elsevier, vol. 146(1), pages 248-274, January.
  6. Gaurab Aryal & Ronald Stauber, 2013. "Trembles in Extensive Games with Ambiguity Averse Players," ANU Working Papers in Economics and Econometrics, Australian National University, College of Business and Economics, School of Economics 2013-606, Australian National University, College of Business and Economics, School of Economics.
  7. : Kostas Koufopoulos & : Roman Kozhan, 2012. "Optimal Insurance under Advserse Selection and Ambiguity Aversion," Working Papers, Warwick Business School, Finance Group wpn12-07, Warwick Business School, Finance Group.
  8. Azrieli, Yaron & Teper, Roee, 2009. "Uncertainty aversion and equilibrium existence in games with incomplete information," MPRA Paper 17617, University Library of Munich, Germany.
  9. Atsushi Kajii & Takashi Ui, 2007. "Interim Efficient Allocations under Uncertainty," KIER Working Papers, Kyoto University, Institute of Economic Research 642, Kyoto University, Institute of Economic Research.
  10. Ronald Stauber, 2014. "A framework for robustness to ambiguity of higher-order beliefs," International Journal of Game Theory, Springer, Springer, vol. 43(3), pages 525-550, August.
  11. De Marco, Giuseppe & Romaniello, Maria, 2013. "A limit theorem for equilibria under ambiguous belief correspondences," Mathematical Social Sciences, Elsevier, Elsevier, vol. 66(3), pages 431-438.

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