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On Games and Equilibria with Coherent Lower Expectations

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  • Giuseppe De Marco
  • Maria Romaniello

Abstract

Different solution concepts for strategic form games have been introduced in order to weaken the consistency assumption that players’ beliefs, about their opponents strategic choices, are correct in equilibrium. The literature has shown that ambiguous beliefs are an appropriate device to deal with this task. In this note, we introduce an equilibrium concept in which players do not know the opponents’ strategies in their entirety but only the coherent lower expectations of some random variables that depend on the actual strategies taken by the others. This equilibrium concept generalizes the already existing concept of equilibrium with partially specified probabilities by extending the set of feasible beliefs and allowing for comparative probability judgements. We study the issue of the existence of the equilibrium points in our framework and find sufficient conditions which involve the continuity of coherent lower expectations and a Slater-like condition for the systems of inequalities defining beliefs.

Suggested Citation

  • Giuseppe De Marco & Maria Romaniello, 2015. "On Games and Equilibria with Coherent Lower Expectations," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-8, June.
    • Handle: RePEc:hin:jnlmpe:690295
    DOI: 10.1155/2015/690295
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    References listed on IDEAS

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    1. Jürgen Eichberger & David Kelsey & Burkhard C. Schipper, 2009. "Ambiguity and social interaction," Oxford Economic Papers, Oxford University Press, vol. 61(2), pages 355-379, April.
    2. Lo, Kin Chung, 1996. "Equilibrium in Beliefs under Uncertainty," Journal of Economic Theory, Elsevier, vol. 71(2), pages 443-484, November.
    3. Ehud Lehrer, 2012. "Partially Specified Probabilities: Decisions and Games," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 70-100, February.
    4. Ebbe Groes & Hans Jørgen Jacobsen & Birgitte Sloth & Torben Tranaes, 1998. "Nash Equilibrium with Lower Probabilities," Theory and Decision, Springer, vol. 44(1), pages 37-66, January.
    5. 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.
    6. Marinacci, Massimo, 2000. "Ambiguous Games," Games and Economic Behavior, Elsevier, vol. 31(2), pages 191-219, May.
    7. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February.
    8. 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.
    9. 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.
    10. Friedman, James W. & Mezzetti, Claudio, 2005. "Random belief equilibrium in normal form games," Games and Economic Behavior, Elsevier, vol. 51(2), pages 296-323, May.
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    Cited by:

    1. 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.

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