Coalitional Expected Multi-Utility Theory

Kazuhiro Hara, Efe A. Ok, Gil Riella

    Research output: Contribution to journalArticlepeer-review

    Abstract

    This paper begins by observing that any reflexive binary (preference) relation (over risky prospects) that satisfies the independence axiom admits a form of expected utility representation. We refer to this representation notion as the coalitional minmax expected utility representation. By adding the remaining properties of the expected utility theorem, namely, continuity, completeness, and transitivity, one by one, we find how this representation gets sharper and sharper, thereby deducing the versions of this classical theorem in which any combination of these properties is dropped from its statement. This approach also allows us to weaken transitivity in this theorem, rather than eliminate it entirely, say, to quasitransitivity or acyclicity. Apart from providing a unified dissection of the expected utility theorem, these results are relevant for the growing literature on boundedly rational choice in which revealed preference relations often lack the properties of completeness and/or transitivity (but often satisfy the independence axiom). They are also especially suitable for the (yet overlooked) case in which the decision-maker is made up of distinct individuals and, consequently, transitivity is routinely violated. Finally, and perhaps more importantly, we show that our representation theorems allow us to answer many economic questions that are posed in terms of nontransitive/incomplete preferences, say, about the maximization of preferences, the existence of Nash equilibrium, the preference for portfolio diversification, and the possibility of the preference reversal phenomenon.

    Original languageEnglish (US)
    Pages (from-to)933-980
    Number of pages48
    JournalEconometrica
    Volume87
    Issue number3
    DOIs
    StatePublished - May 2019

    Keywords

    • Affine binary relations
    • existence of mixed strategy Nash equilibrium
    • justifiable preferences
    • nontransitive and incomplete expected utility representations
    • preference for portfolio diversification
    • preference reversal phenomenon

    ASJC Scopus subject areas

    • Economics and Econometrics

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