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Uncertain acts in games
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Uncertain acts in games

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  • Riedel, Frank

    (Center for Mathematical Economics, Bielefeld University)

Abstract

This text reviews a recent approach to modeling "radically uncertain" behavior in strategic interactions. By rigorously rooting the approach in decision theory, we provide a foundation for applications of Knightian uncertainty in mechanism design, principal agent and moral hazard models. We discuss critical assessments and provide alternative interpretations of the new equilibria in terms of equilibrium in beliefs, and as a boundedly rational equilibrium in the sense of a population equilibrium. We also discuss the purification of equilibria in the spirit of Harsanyi.

Suggested Citation

  • Riedel, Frank, 2017. "Uncertain acts in games," Center for Mathematical Economics Working Papers 571, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:571
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    File URL: https://pub.uni-bielefeld.de/download/2909171/2909172
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    References listed on IDEAS

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    1. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    2. Riedel, Frank, 2004. "Dynamic coherent risk measures," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 185-200, August.
    3. Decerf, Benoit & Riedel, Frank, 2016. "Disambiguation of Ellsberg equilibria in 2x2 normal form games," Center for Mathematical Economics Working Papers 554, Center for Mathematical Economics, Bielefeld University.
    4. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    5. Lo, Kin Chung, 1996. "Equilibrium in Beliefs under Uncertainty," Journal of Economic Theory, Elsevier, vol. 71(2), pages 443-484, November.
    6. Jacob K. Goeree & Charles A. Holt, 2001. "Ten Little Treasures of Game Theory and Ten Intuitive Contradictions," American Economic Review, American Economic Association, vol. 91(5), pages 1402-1422, December.
    7. ,, 2014. "Second order beliefs models of choice under imprecise risk: non-additive second order beliefs vs. nonlinear second order utility," Theoretical Economics, Econometric Society, vol. 9(3), September.
    8. Kellner, Christian & Le Quement, Mark T., 2018. "Endogenous ambiguity in cheap talk," Journal of Economic Theory, Elsevier, vol. 173(C), pages 1-17.
    9. Bade, Sophie, 2011. "Ambiguous act equilibria," Games and Economic Behavior, Elsevier, vol. 71(2), pages 246-260, March.
    10. Sass, Linda, 2014. "Kuhn's Theorem for Extensive Form Ellsberg Games," Center for Mathematical Economics Working Papers 478, Center for Mathematical Economics, Bielefeld University.
    11. repec:oup:restud:v:84:y::i:1:p:237-276. is not listed on IDEAS
    12. Aryal, Gaurab & Stauber, Ronald, 2014. "A note on Kuhn’s Theorem with ambiguity averse players," Economics Letters, Elsevier, vol. 125(1), pages 110-114.
    13. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    14. Robert Aumann & Adam Brandenburger, 2014. "Epistemic Conditions for Nash Equilibrium," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 5, pages 113-136, World Scientific Publishing Co. Pte. Ltd..
    15. Subir Bose & Ludovic Renou, 2014. "Mechanism Design With Ambiguous Communication Devices," Econometrica, Econometric Society, vol. 82, pages 1853-1872, September.
    16. 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.
    17. Lang, Matthias & Wambach, Achim, 2013. "The fog of fraud – Mitigating fraud by strategic ambiguity," Games and Economic Behavior, Elsevier, vol. 81(C), pages 255-275.
    18. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    19. Frank Riedel & Linda Sass, 2014. "Ellsberg games," Theory and Decision, Springer, vol. 76(4), pages 469-509, April.
    20. 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.
    21. Kellner, Christian & Le Quement, Mark T., 2018. "Endogenous ambiguity in cheap talk," Journal of Economic Theory, Elsevier, vol. 173(C), pages 1-17.
    22. Marinacci, Massimo, 2000. "Ambiguous Games," Games and Economic Behavior, Elsevier, vol. 31(2), pages 191-219, May.
    23. 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.
    24. Stauber, Ronald, 2017. "Irrationality and ambiguity in extensive games," Games and Economic Behavior, Elsevier, vol. 102(C), pages 409-432.
    25. Alfredo di Tillio & Nenad Kos & Matthias Messner, 2017. "The Design of Ambiguous Mechanisms," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 84(1), pages 237-276.
    26. 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.
    27. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    28. Raphaël Giraud, 2014. "Second order beliefs models of choice under imprecise risk: Nonadditive second order beliefs versus nonlinear second order utility," Post-Print halshs-00102346, HAL.
    29. Grant, Simon & Meneghel, Idione & Tourky, Rabee, 2016. "Savage games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    30. Sarin, Rakesh & Wakker, Peter P, 1998. "Dynamic Choice and NonExpected Utility," Journal of Risk and Uncertainty, Springer, vol. 17(2), pages 87-119, November.
    31. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
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    Cited by:

    1. Benoit Decerf & Frank Riedel, 2020. "Purification and disambiguation of Ellsberg equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(3), pages 595-636, April.
    2. Demeze-Jouatsa, Ghislain-Herman, 2018. "Repetition and cooperation: A model of finitely repeated games with objective ambiguity," Center for Mathematical Economics Working Papers 585, Center for Mathematical Economics, Bielefeld University.
    3. Kellner, Christian & Le Quement, Mark T., 2018. "Endogenous ambiguity in cheap talk," Journal of Economic Theory, Elsevier, vol. 173(C), pages 1-17.

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    More about this item

    Keywords

    Knightian Uncertainty in Games; Strategic Ambiguity; Ellsberg Games; Purification;
    All these keywords.

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