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Subjective expected utility in games

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    (Department of Economics and IGIER, Università Bocconi)

Abstract

This paper extends Savage's subjective approach to probability and utility from decision problems under exogenous uncertainty to choice in strategic environments. Interactive uncertainty is modeled both explicitly, using hierarchies of preference relations, the analogue of beliefs hierarchies, and implicitly, using preference structures, the analogue of type spaces a la Harsanyi, and it is shown that the two approaches are equivalent. Preference structures can be seen as those sets of hierarchies arising when certain restrictions on preferences, along with the players' common certainty of the restrictions, are imposed. Preferences are a priori assumed to satisfy only very mild properties (reflexivity, transitivity, and monotone continuity). Thus, the results provide a framework for the analysis of behavior in games under essentially any axiomatic structure. An explicit characterization is given for Savage's axioms, and it is shown that a hierarchy of relatively simple preference relations uniquely identifies the decision maker's utilities and beliefs of all orders. Connections with the literature on beliefs hierarchies and correlated equilibria are discussed.

Suggested Citation

  • ,, 2008. "Subjective expected utility in games," Theoretical Economics, Econometric Society, vol. 3(3), September.
  • Handle: RePEc:the:publsh:302
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    Cited by:

    1. Bonanno, Giacomo & Tsakas, Elias, 2018. "Common belief of weak-dominance rationality in strategic-form games: A qualitative analysis," Games and Economic Behavior, Elsevier, vol. 112(C), pages 231-241.
    2. Fukuda, Satoshi, 2024. "The existence of universal qualitative belief spaces," Journal of Economic Theory, Elsevier, vol. 216(C).
    3. Ganguli, Jayant & Heifetz, Aviad & Lee, Byung Soo, 2016. "Universal interactive preferences," Journal of Economic Theory, Elsevier, vol. 162(C), pages 237-260.
    4. Grant, Simon & Meneghel, Idione & Tourky, Rabee, 2013. "Savage Games: A Theory of Strategic Interaction with Purely Subjective Uncertainty," Risk and Sustainable Management Group Working Papers 151501, University of Queensland, School of Economics.
    5. Bergemann, Dirk & Morris, Stephen & Takahashi, Satoru, 2017. "Interdependent preferences and strategic distinguishability," Journal of Economic Theory, Elsevier, vol. 168(C), pages 329-371.
    6. Willemien Kets, 2012. "Bounded Reasoning and Higher-Order Uncertainty," Discussion Papers 1547, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. Ziegler, Gabriel & Zuazo-Garin, Peio, 2020. "Strategic cautiousness as an expression of robustness to ambiguity," Games and Economic Behavior, Elsevier, vol. 119(C), pages 197-215.
    8. Michael Trost, 2013. "Epistemic characterizations of iterated deletion of inferior strategy profiles in preference-based type spaces," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 755-776, August.
    9. Friedenberg, Amanda, 2010. "When do type structures contain all hierarchies of beliefs?," Games and Economic Behavior, Elsevier, vol. 68(1), pages 108-129, January.
    10. Galeazzi, Paolo & Marti, Johannes, 2023. "Choice structures in games," Games and Economic Behavior, Elsevier, vol. 140(C), pages 431-455.
    11. Stephen Morris & Satoru Takahashi, 2011. "Common Certainty of Rationality Revisited," Working Papers 1301, Princeton University, Department of Economics, Econometric Research Program..
    12. Grant, Simon & Meneghel, Idione & Tourky, Rabee, 2016. "Savage games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    13. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    14. Stephen Morris & Satoru Takahashi, 2012. "Games in Preference Form and Preference Rationalizability," Working Papers 1420, Princeton University, Department of Economics, Econometric Research Program..
    15. Paolo Galeazzi & Johannes Marti, 2023. "Choice Structures in Games," Papers 2304.11575, arXiv.org.
    16. repec:esx:essedp:722 is not listed on IDEAS
    17. Chen, Yi-Chun, 2010. "Universality of the Epstein-Wang type structure," Games and Economic Behavior, Elsevier, vol. 68(1), pages 389-402, January.
    18. Lee, Byung Soo, 2016. "A space of lexicographic preferences," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 16-25.
    19. Azrieli, Yaron & Teper, Roee, 2011. "Uncertainty aversion and equilibrium existence in games with incomplete information," Games and Economic Behavior, Elsevier, vol. 73(2), pages 310-317.
    20. Yang, Jian, 2018. "Game-theoretic modeling of players’ ambiguities on external factors," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 31-56.
    21. Aviad Heifetz & Willemien Kets, 2012. "All Types Naive and Canny," Discussion Papers 1550, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

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    More about this item

    Keywords

    Subjective probability; preference hierarchies; type spaces; beliefs hierarchies; common belief; expected utility; incomplete information; correlated equilibria;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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