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Sequential two-player games with ambiguity

Author

Listed:
  • Eichberger, Jürgen
  • Kelsey, David
Abstract
If players' beliefs are strictly non-additive, the Dempster-Shafer updating rule can be used to define beliefs off the equilibrium path. We define an equilibrium concept in sequential two-person games where players update their beliefs with the Dempster-Shafer updating rule. We show that in the limit as uncertainty tends to zero, our equilibrium approximates Bayesian Nash equilibrium by imposing context-dependent constraints on beliefs under uncertainty.

Suggested Citation

  • Eichberger, Jürgen & Kelsey, David, 2003. "Sequential two-player games with ambiguity," Papers 03-27, Sonderforschungsbreich 504.
    • Handle: RePEc:mnh:spaper:2758
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    File URL: https://madoc.bib.uni-mannheim.de/2758/1/dp03_27.pdf
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    References listed on IDEAS

    as
    1. Ryan, Matthew J., 2002. "Violations of Belief Persistence in Dempster-Shafer Equilibrium," Games and Economic Behavior, Elsevier, vol. 39(1), pages 167-174, April.
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    7. 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.
    8. Lo, Kin Chung, 1999. "Extensive Form Games with Uncertainty Averse Players," Games and Economic Behavior, Elsevier, vol. 28(2), pages 256-270, August.
    9. Marinacci, Massimo, 2000. "Ambiguous Games," Games and Economic Behavior, Elsevier, vol. 31(2), pages 191-219, May.
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    13. Eichberger, Jurgen & Kelsey, David, 2002. "Strategic Complements, Substitutes, and Ambiguity: The Implications for Public Goods," Journal of Economic Theory, Elsevier, vol. 106(2), pages 436-466, October.
    14. Camerer, Colin & Weber, Martin, 1992. "Recent Developments in Modeling Preferences: Uncertainty and Ambiguity," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 325-370, October.
    15. Brandts, Jordi & Holt, Charles A, 1992. "An Experimental Test of Equilibrium Dominance in Signaling Games," American Economic Review, American Economic Association, vol. 82(5), pages 1350-1365, December.
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    19. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February.
    20. Jürgen Eichberger & David Kelsey, 1999. "E-Capacities and the Ellsberg Paradox," Theory and Decision, Springer, vol. 46(2), pages 107-138, April.
    21. John Creedy & Jeff Borland & Jürgen Eichberger, 1992. "Recent Developments In Game Theory," Books, Edward Elgar Publishing, number 115.
    22. Michael Spence, 1973. "Job Market Signaling," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 87(3), pages 355-374.
    Full references (including those not matched with items on IDEAS)

    Citations

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    as


    Cited by:

    1. Eichberger, Jürgen & Grant, Simon & Lefort, Jean-Philippe, 2008. "Neo-additive capacities and updating," Sonderforschungsbereich 504 Publications 08-31, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
    2. Stauber, Ronald, 2017. "Irrationality and ambiguity in extensive games," Games and Economic Behavior, Elsevier, vol. 102(C), pages 409-432.
    3. Jürgen Eichberger & David Kelsey, 2011. "Are the treasures of game theory ambiguous?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 313-339, October.
    4. Eran Hanany & Peter Klibanoff & Sujoy Mukerji, 2020. "Incomplete Information Games with Ambiguity Averse Players," American Economic Journal: Microeconomics, American Economic Association, vol. 12(2), pages 135-187, May.
    5. Adam Dominiak & Ani Guerdjikova, 2021. "Special Issue on Ambiguity and Strategic Interactions in Honor of Jürgen Eichberger," Theory and Decision, Springer, vol. 90(3), pages 301-307, May.
    6. Dominiak, Adam & Lee, Min Suk, 2017. "Coherent Dempster–Shafer equilibrium and ambiguous signals," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 42-54.
    7. repec:awi:wpaper:0469 is not listed on IDEAS
    8. Dominiak, Adam & Eichberger, Jürgen, 2021. "Games in context: Equilibrium under ambiguity for belief functions," Games and Economic Behavior, Elsevier, vol. 128(C), pages 125-159.
    9. Pulford, Briony D. & Colman, Andrew M., 2007. "Ambiguous games: Evidence for strategic ambiguity aversion," MPRA Paper 86345, University Library of Munich, Germany.
    10. Roman Kozhan, 2011. "Non-additive anonymous games," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 215-230, May.

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    More about this item

    Keywords

    Uncertainty-aversion ; capacity ; Dempster-Shafer rule ; bargaining ; signalling game;
    All these keywords.

    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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