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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.

Suggested Citation

  • Azrieli, Yaron & Teper, Roee, 2009. "Uncertainty aversion and equilibrium existence in games with incomplete information," MPRA Paper 17617, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:17617
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    Citations

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    Cited by:

    1. Frank Riedel & Linda Sass, 2014. "Ellsberg games," Theory and Decision, Springer, vol. 76(4), pages 469-509, April.
    2. Giuseppe De Marco, 2016. "Ambiguous Games without a State Space and Full Rationality," CSEF Working Papers 425, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy, revised 01 Apr 2017.
    3. Eichberger, Jürgen & Grant, Simon & Kelsey, David, 2017. "Ambiguity and the Centipede Game: Strategic Uncertainty in Multi-Stage Games," Working Papers 0638, University of Heidelberg, Department of Economics.
    4. Bade, Sophie, 2011. "Ambiguous act equilibria," Games and Economic Behavior, Elsevier, vol. 71(2), pages 246-260, March.
    5. Calford, Evan, 2016. "Mixed Strategies in Games with Ambiguity Averse Agents," MPRA Paper 74909, University Library of Munich, Germany.
    6. Gaurab Aryal & Ronald Stauber, 2014. "Trembles in extensive games with ambiguity averse players," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(1), pages 1-40, September.
    7. Stauber, Ronald, 2017. "Irrationality and ambiguity in extensive games," Games and Economic Behavior, Elsevier, vol. 102(C), pages 409-432.
    8. Giuseppe De Marco & Maria Romaniello, 2014. "Variational Preferences and Equilibria in Games under Ambiguous Beliefs Correspondences," CSEF Working Papers 363, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    9. Dorian Beauchêne, 2016. "Solution concepts for games with ambiguous payoffs," Theory and Decision, Springer, vol. 80(2), pages 245-269, February.
    10. Muraviev, Igor & Riedel, Frank & Sass, Linda, 2017. "Kuhn’s Theorem for extensive form Ellsberg games," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 26-41.
    11. repec:eee:gamebe:v:104:y:2017:i:c:p:271-292 is not listed on IDEAS
    12. Alfredo Di Tillio & Nenad Kos & Matthias Messner, 2012. "The Design of Ambiguous Mechanisms," Working Papers 446, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    13. Grant, Simon & Meneghel, Idione & Tourky, Rabee, 2016. "Savage games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    14. Dominiak, Adam & Lee, Min Suk, 2017. "Coherent Dempster–Shafer equilibrium and ambiguous signals," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 42-54.
    15. Kauffeldt, T. Florian, 2016. "Strategic behavior of non-expected utility players in games with payoff uncertainty," Working Papers 0614, University of Heidelberg, Department of Economics.

    More about this item

    Keywords

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

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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