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Scalarization Methods and Expected Multi-Utility Representations

Author

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  • Özgür Evren

    (New Economic School)

Abstract
I characterize the class of (possibly incomplete) preference relations over lotteries which can be represented by a compact set of (continuous) expected utility functions that preserve both indifferences and strict preferences. This finding contrasts with the representation theorem of Dubra, Maccheroni and Ok (2004) which typically delivers some functions which do not respect strict preferences. For a preference relation of the sort that I consider in this paper, my representation theorem reduces the problem of recovering the associated choice correspondence over convex sets of lotteries to a scalar-valued, parametric optimization exercise. By utilizing this scalarization method, I also provide characterizations of some solution concepts. Most notably, I show that in an otherwise standard game with incomplete preferences, the collection of pure strategy equilibria that one can find using this scalarization method corresponds to a refinement of the notion of Nash equilibrium that requires the (deterministic) action of each player be undominated by any mixed strategy that she can follow, given others’ actions.

Suggested Citation

  • Özgür Evren, 2012. "Scalarization Methods and Expected Multi-Utility Representations," Working Papers w0174, New Economic School (NES).
    • Handle: RePEc:abo:neswpt:w0174
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    File URL: https://www.nes.ru/files/Preprints-resh/WP174.pdf
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    References listed on IDEAS

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    Cited by:

    1. repec:hal:pseose:halshs-01415412 is not listed on IDEAS
    2. Leandro Gorno, 2018. "The structure of incomplete preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(1), pages 159-185, July.
    3. Eric Danan & Thibault Gajdos & Brian Hill & Jean-Marc Tallon, 2016. "Robust Social Decisions," American Economic Review, American Economic Association, vol. 106(9), pages 2407-2425, September.
    4. Gorno, Leandro, 2017. "A strict expected multi-utility theorem," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 92-95.
    5. Evren, Özgür, 2014. "Scalarization methods and expected multi-utility representations," Journal of Economic Theory, Elsevier, vol. 151(C), pages 30-63.
    6. José Carlos R. Alcantud & Gianni Bosi & Magalì Zuanon, 2016. "Richter–Peleg multi-utility representations of preorders," Theory and Decision, Springer, vol. 80(3), pages 443-450, March.
    7. repec:ipg:wpaper:2014-060 is not listed on IDEAS
    8. G. Carlier & R.-A. Dana & R.-A. Dana, 2014. "Pareto optima and equilibria when preferences are incompletely known," Working Papers 2014-60, Department of Research, Ipag Business School.
    9. repec:ipg:wpaper:59 is not listed on IDEAS
    10. Simone Cerreia-Vioglio & Efe A. Ok, 2018. "The Rational Core of Preference Relations," Working Papers 632, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.

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    More about this item

    Keywords

    Incomplete preference relations; Expected Utility; Nash Equilibrium; Nonbinary Choice; Social Planning; Incomplete Knowledge;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis

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