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Finitely additive behavioral strategies: when do they induce an unambiguous expected payoff?

Author

Listed:
  • János Flesch

    (Maastricht University)

  • Dries Vermeulen

    (Maastricht University)

  • Anna Zseleva

    (Maastricht University)

Abstract

We examine infinite horizon decision problems with arbitrary bounded payoff functions in which the decision maker uses finitely additive behavioral strategies. Since we only assume that the payoff function is bounded, it is well-known that these behavioral strategies generally do not induce unambiguously defined expected payoffs. Consequently, it is not clear how to compare behavioral strategies and define optimality. We address this problem by finding conditions on the payoff function that guarantee an unambiguous expected payoff regardless of which behavioral strategy the decision maker uses. To this end, we systematically consider various alternatives proposed in the literature on how to define the finitely additive probability measure on the set of infinite plays induced by a behavioral strategy.

Suggested Citation

  • János Flesch & Dries Vermeulen & Anna Zseleva, 2024. "Finitely additive behavioral strategies: when do they induce an unambiguous expected payoff?," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(2), pages 695-723, June.
    • Handle: RePEc:spr:jogath:v:53:y:2024:i:2:d:10.1007_s00182-024-00892-5
    DOI: 10.1007/s00182-024-00892-5
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    References listed on IDEAS

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    1. A. Maitra & W. Sudderth, 1998. "Finitely additive stochastic games with Borel measurable payoffs," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(2), pages 257-267.
    2. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Schmeidler, David, 2022. "Equilibria of nonatomic anonymous games," Games and Economic Behavior, Elsevier, vol. 135(C), pages 110-131.
    3. Capraro, Valerio & Scarsini, Marco, 2013. "Existence of equilibria in countable games: An algebraic approach," Games and Economic Behavior, Elsevier, vol. 79(C), pages 163-180.
    4. Harris, Christopher J. & Stinchcombe, Maxwell B. & Zame, William R., 2005. "Nearly compact and continuous normal form games: characterizations and equilibrium existence," Games and Economic Behavior, Elsevier, vol. 50(2), pages 208-224, February.
    5. William D. Sudderth, 2016. "Finitely Additive Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 92-108, February.
    6. Maitra, A & Sudderth, W, 1993. "Finitely Additive and Measurable Stochastic Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(3), pages 201-223.
    7. Nabil I. Al-Najjar, 2009. "Decision Makers as Statisticians: Diversity, Ambiguity, and Learning," Econometrica, Econometric Society, vol. 77(5), pages 1371-1401, September.
    8. Oliver Schirokauer & Joseph B. Kadane, 2007. "Uniform Distributions on the Natural Numbers," Journal of Theoretical Probability, Springer, vol. 20(3), pages 429-441, September.
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    More about this item

    Keywords

    Infinite duration decision problem; Behavioral strategy; Expected payoff; Finitely additive probability measure;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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