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A Derivation of Expected Utility Maximization in the Context of a Game

Author

Listed:
  • Itzhak Gilboa

    (Tel Aviv University)

  • David Schmeidler

    (Tel Aviv University)

Abstract

A decision maker faces a decision problem, or a game against nature. For each probability distribution over the state of the world (nature's strategies), she has a weak order over her acts (pure strategies). We formulate conditions on these weak orders guaranteeing that they can be jointly represented by expected utility maximization with respect to an almost-unique state-dependent utility, that is, a matrix assigning real numbers to act-state pairs. As opposed to a utility function that is derived in another context, the utility matrix derived in the game will incorporate all psychological or sociological determinants of well-being that result from the very fact that the outcomes are obtained in a given game.

Suggested Citation

  • Itzhak Gilboa & David Schmeidler, 2001. "A Derivation of Expected Utility Maximization in the Context of a Game," Cowles Foundation Discussion Papers 1342, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1342
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    2. Perea, Andrés, 2025. "Dynamic consistency in games without expected utility," Journal of Economic Theory, Elsevier, vol. 229(C).
    3. Salonia, Enrico Mattia, 2024. "A Foundation for Universalisation in Games," TSE Working Papers 24-1586, Toulouse School of Economics (TSE).
    4. Mehmet S. Ismail & Ronald Peeters, 2023. "Social preferences and expected utility," Papers 2312.06048, arXiv.org.
    5. Brandl, Florian & Brandt, Felix, 2019. "Justifying optimal play via consistency," Theoretical Economics, Econometric Society, vol. 14(4), November.
    6. Pierfrancesco Guarino, 2023. "Revealing Sequential Rationality and Forward Induction," Papers 2312.03536, arXiv.org.
    7. Azrieli, Yaron, 2011. "Axioms for Euclidean preferences with a valence dimension," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 545-553.
    8. Florian Brandl & Felix Brandt, 2023. "A Robust Characterization of Nash Equilibrium," Papers 2307.03079, arXiv.org, revised Jun 2024.
    9. Brandl, Florian & Brandt, Felix, 2024. "An axiomatic characterization of Nash equilibrium," Theoretical Economics, Econometric Society, vol. 19(4), November.
    10. O'Callaghan, Patrick, 2016. "Parametric continuity from preferences when the topology is weak and actions are discrete," MPRA Paper 72356, University Library of Munich, Germany.
    11. O'Callaghan, Patrick, 2011. "Context and Decision: Utility on a Union of Mixture Spaces," Economic Research Papers 270751, University of Warwick - Department of Economics.
    12. O'Callaghan, Patrick, 2016. "Minimal conditions for parametric continuity and stable policy in extreme settings," MPRA Paper 70989, University Library of Munich, Germany.
    13. O'Callaghan, Patrick, "undated". "Ordinal, nonlinear context dependence," Risk and Sustainable Management Group Working Papers 152450, University of Queensland, School of Economics.
    14. Castillo, Marco E. & Cross, Philip J., 2008. "Of mice and men: Within gender variation in strategic behavior," Games and Economic Behavior, Elsevier, vol. 64(2), pages 421-432, November.
    15. Marciano Siniscalchi, 2022. "Structural Rationality in Dynamic Games," Econometrica, Econometric Society, vol. 90(5), pages 2437-2469, September.
    16. Castillo, Marco E. & Cross, Philip J. & Freer, Mikhail, 2019. "Nonparametric utility theory in strategic settings: Revealing preferences and beliefs from proposal–response games," Games and Economic Behavior, Elsevier, vol. 115(C), pages 60-82.
    17. Grant, Simon & Meneghel, Idione & Tourky, Rabee, 2016. "Savage games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    18. O’Callaghan, Patrick H., 2017. "Axioms for parametric continuity of utility when the topology is coarse," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 88-94.
    19. O’Callaghan, Patrick, 2011. "Context and Decision: Utility on a Union of Mixture Spaces," The Warwick Economics Research Paper Series (TWERPS) 973, University of Warwick, Department of Economics.
    20. Chambers, Christopher P. & Hayashi, Takashi, 2012. "Choice and individual welfare," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1818-1849.
    21. Li, Chen & Turmunkh, Uyanga & Wakker, Peter P., 2020. "Social and strategic ambiguity versus betrayal aversion," Games and Economic Behavior, Elsevier, vol. 123(C), pages 272-287.
    22. Andrés Perea, 2025. "Expected utility as an expression of linear preference intensity," Theory and Decision, Springer, vol. 98(4), pages 561-598, June.

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    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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