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Scalarization methods and expected multi-utility representations

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  • Evren, Özgür
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 [16] 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 not worse than any mixed strategy that she can follow, given others' actions.

Suggested Citation

  • Evren, Özgür, 2014. "Scalarization methods and expected multi-utility representations," Journal of Economic Theory, Elsevier, vol. 151(C), pages 30-63.
    • Handle: RePEc:eee:jetheo:v:151:y:2014:i:c:p:30-63
    DOI: 10.1016/j.jet.2014.02.003
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    More about this item

    Keywords

    Incomplete preferences; Expected utility; Nash equilibrium; Nonbinary choice; Maxmin under risk; Pareto efficiency;
    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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