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Subjective Uncertainty Over Behavior Strategies: A Correction

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  • Eddie Dekel
  • Drew Fudenberg
  • David K Levine

Abstract

In order to model the subjective uncertainty of a player over the behavior strategies of an opponent, one must consider the player's beliefs about the opponent's play at information sets that the player thinks have probability zero. This corregendum uses “trembles†to provide a definition of the convex hull of a set of behavior strategies. This corrects a definition we gave in [E. Dekel, D. Fudenberg, and D. K. Levine, 1999, J. Econ. Theory 89, 165–185], which led to two of the solution concepts we defined there not having the properties we intended.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Eddie Dekel & Drew Fudenberg & David K Levine, 2001. "Subjective Uncertainty Over Behavior Strategies: A Correction," Levine's Working Paper Archive 7571, David K. Levine.
    • Handle: RePEc:cla:levarc:7571
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    File URL: http://www.dklevine.com/papers/conhullrev20.pdf
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    References listed on IDEAS

    as
    1. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    2. Dekel, Eddie & Fudenberg, Drew & Levine, David K., 1999. "Payoff Information and Self-Confirming Equilibrium," Journal of Economic Theory, Elsevier, vol. 89(2), pages 165-185, December.
    3. D. Pearce, 2010. "Rationalizable Strategic Behavior and the Problem of Perfection," Levine's Working Paper Archive 523, David K. Levine.
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    7. Asheim,G.B. & Perea,A., 2000. "Lexicographic probabilities and rationalizability in extensive games," Memorandum 38/2000, Oslo University, Department of Economics.
    8. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    9. Roger B. Myerson, 1986. "Axiomatic Foundations of Bayesian Decision Theory," Discussion Papers 671, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    10. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January.
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    Cited by:

    1. Schipper, Burkhard C., 2021. "Discovery and equilibrium in games with unawareness," Journal of Economic Theory, Elsevier, vol. 198(C).
    2. Giacomo Bonanno, 2022. "Rational Play in Extensive-Form Games," Games, MDPI, vol. 13(6), pages 1-20, October.
    3. Joseph Greenberg & Sudheer Gupta & Xiao Luo, 2003. "Towering over Babel: Worlds Apart but Acting Together," IEAS Working Paper : academic research 03-A009, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    4. Sheng-Chieh Huang & Xiao Luo, 2008. "Stability, sequential rationality, and subgame consistency," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 34(2), pages 309-329, February.
    5. Joseph Greenberg & Sudheer Gupta & Xiao Luo, 2009. "Mutually acceptable courses of action," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(1), pages 91-112, July.
    6. Asheim, Geir B. & Brunnschweiler, Thomas, 2023. "Epistemic foundation of the backward induction paradox," Games and Economic Behavior, Elsevier, vol. 141(C), pages 503-514.
    7. Jagau, Stephan & Perea, Andrés, 2022. "Common belief in rationality in psychological games," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    8. , & ,, 2015. "Rationalizable partition-confirmed equilibrium," Theoretical Economics, Econometric Society, vol. 10(3), September.
    9. Perea, Andrés, 2014. "Belief in the opponentsʼ future rationality," Games and Economic Behavior, Elsevier, vol. 83(C), pages 231-254.
    10. Giacomo Bonanno, 2013. "An epistemic characterization of generalized backward induction," Working Papers 132, University of California, Davis, Department of Economics.
    11. Giacomo Bonanno, 2021. "Rational play in games: A behavioral approach," Working Papers 344, University of California, Davis, Department of Economics.
    12. Xiao Luo & Ben Wang, 2022. "An epistemic characterization of MACA," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(4), pages 995-1024, June.
    13. Asheim, Geir B. & Perea, Andres, 2005. "Sequential and quasi-perfect rationalizability in extensive games," Games and Economic Behavior, Elsevier, vol. 53(1), pages 15-42, October.
    14. Chlaß, Nadine & Perea, Andrés, 2016. "How do people reason in dynamic games?," VfS Annual Conference 2016 (Augsburg): Demographic Change 145881, Verein für Socialpolitik / German Economic Association.
    15. Iryna Topolyan, 2020. "On Common Belief in Future Rationality in Games with Ambiguous Orderings of Information Sets," Dynamic Games and Applications, Springer, vol. 10(1), pages 183-201, March.
    16. Xiao Luo & Xuewen Qian & Yang Sun, 2021. "The algebraic geometry of perfect and sequential equilibrium: an extension," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 579-601, March.
    17. Rubén Becerril-Borja & Andrés Perea, 2020. "Common belief in future and restricted past rationality," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(3), pages 711-747, September.
    18. Giacomo Bonanno, 2013. "An epistemic characterization of generalized backward induction," Working Papers 60, University of California, Davis, Department of Economics.

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