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Ambiguous Games without a State Space and Full Rationality

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Abstract

Aim of this paper to differentiate and to better understand the assumptions that must be imposed on the structure of ambiguity and on the attitudes towards ambiguity in order to have the existence of equilibria in games under ambiguous belief correspondences. In the present paper, this class of games is studied under weaker restrictions on preferences which are not required to be rational. This paper shows that the assumption of imprecision averse (resp. loving) preferences is key to obtain equilibrium existence whenever it is combined with the property of convexity (resp. concavity) of the ambiguous belief correspondences. The paper also studies the role played by these assumptions in different specific models, so as to illustrate the applicability of the results of equilibrium existence.

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  • 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.
  • Handle: RePEc:sef:csefwp:425
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    References listed on IDEAS

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    1. Lo, Kin Chung, 1996. "Equilibrium in Beliefs under Uncertainty," Journal of Economic Theory, Elsevier, vol. 71(2), pages 443-484, November.
    2. Bade, Sophie, 2011. "Ambiguous act equilibria," Games and Economic Behavior, Elsevier, vol. 71(2), pages 246-260, March.
    3. Gajdos, Thibault & Tallon, Jean-Marc & Vergnaud, Jean-Christophe, 2004. "Decision making with imprecise probabilistic information," Journal of Mathematical Economics, Elsevier, vol. 40(6), pages 647-681, September.
    4. David S. Ahn, 2008. "Ambiguity Without a State Space," Review of Economic Studies, Oxford University Press, vol. 75(1), pages 3-28.
    5. Giuseppe De Marco & Maria Romaniello, 2015. "On Games and Equilibria with Coherent Lower Expectations," CSEF Working Papers 397, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    6. Gajdos, T. & Hayashi, T. & Tallon, J.-M. & Vergnaud, J.-C., 2008. "Attitude toward imprecise information," Journal of Economic Theory, Elsevier, vol. 140(1), pages 27-65, May.
    7. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
    8. Marinacci, Massimo, 2000. "Ambiguous Games," Games and Economic Behavior, Elsevier, vol. 31(2), pages 191-219, May.
    9. 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.
    10. 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.
    11. 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.
    12. Ehud Lehrer, 2012. "Partially Specified Probabilities: Decisions and Games," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 70-100, February.
    13. De Marco, Giuseppe & Romaniello, Maria, 2013. "A limit theorem for equilibria under ambiguous belief correspondences," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 431-438.
    14. 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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    Cited by:

    1. Giuseppe De Marco, 2019. "On the convexity of preferences in decisions and games under (quasi-)convex/concave imprecise probability correspondences," CSEF Working Papers 523, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.

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