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Uncertainty aversion and equilibrium existence in games with incomplete information

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  • Azrieli, Yaron
  • Teper, Roee

Abstract

We consider games with incomplete information a la Harsanyi, where the payoff of a player depends on an unknown state of nature as well as on the profile of chosen actions. As opposed to the standard model, players' preferences over state--contingent utility vectors are represented by arbitrary functionals. The definitions of Nash and Bayes equilibria naturally extend to this generalized setting. We characterize equilibrium existence in terms of the preferences of the participating players. It turns out that, given continuity and monotonicity of the preferences, equilibrium exists in every game if and only if all players are averse to uncertainty (i.e., all the functionals are quasi--concave). We further show that if the functionals are either homogeneous or translation invariant then equilibrium existence is equivalent to concavity of the functionals.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 17617.

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Date of creation: 29 Sep 2009
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Handle: RePEc:pra:mprapa:17617

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Keywords: Games with incomplete information; equilibrium existence; uncertainty aversion; convex preferences.;

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  1. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, Econometric Society, vol. 55(1), pages 1-18, January.
  2. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 9(3), pages 203-228.
  3. Epstein, Larry G & Wang, Tan, 1996. ""Beliefs about Beliefs" without Probabilities," Econometrica, Econometric Society, Econometric Society, vol. 64(6), pages 1343-73, November.
  4. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2004. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Carlo Alberto Notebooks, Collegio Carlo Alberto 12, Collegio Carlo Alberto, revised 2006.
  5. Andreas Pape & Subir Bose & Emre Ozdenoren, 2004. "Optimal auctions with ambiguity," Econometric Society 2004 North American Summer Meetings, Econometric Society 609, Econometric Society.
  6. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2008. "Uncertainty Averse Preferences," Carlo Alberto Notebooks, Collegio Carlo Alberto 77, Collegio Carlo Alberto.
  7. Epstein, Larry G, 1999. "A Definition of Uncertainty Aversion," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 66(3), pages 579-608, July.
  8. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, INFORMS, vol. 14(3), pages 159-182, November.
  9. Crawford, Vincent P., 1990. "Equilibrium without independence," Journal of Economic Theory, Elsevier, Elsevier, vol. 50(1), pages 127-154, February.
  10. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, Springer, vol. 6(4), pages 429-447.
  11. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  12. Kin Chung Lo, 1998. "Sealed bid auctions with uncertainty averse bidders," Economic Theory, Springer, Springer, vol. 12(1), pages 1-20.
  13. Atsushi Kajii & Takashi Ui, 2005. "Incomplete Information Games With Multiple Priors," The Japanese Economic Review, Japanese Economic Association, Japanese Economic Association, vol. 56(3), pages 332-351.
  14. Sujoy Mukerji & Jean-Marc Tallon, 2003. "An overview of economic applications of David Schmeidler`s models of decision making under uncertainty," Economics Series Working Papers, University of Oxford, Department of Economics 165, University of Oxford, Department of Economics.
  15. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, Elsevier, vol. 102(2), pages 251-289, February.
  16. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  17. Salo, Ahti A & Weber, Martin, 1995. "Ambiguity Aversion in First-Price Sealed-Bid Auctions," Journal of Risk and Uncertainty, Springer, Springer, vol. 11(2), pages 123-37, September.
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Cited by:
  1. Bade, Sophie, 2011. "Ambiguous act equilibria," Games and Economic Behavior, Elsevier, Elsevier, vol. 71(2), pages 246-260, March.
  2. Giuseppe De Marco & Maria Romaniello, 2014. "Variational Preferences and Equilibria in Games under Ambiguous Beliefs Correspondences," CSEF Working Papers, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy 363, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
  3. Riedel, Frank & Sass, Linda, 2013. "Ellsberg Games," Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order, Verein für Socialpolitik / German Economic Association 80012, Verein für Socialpolitik / German Economic Association.

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