 Scalarization Methods and Expected Multi-Utility RepresentationsNo w0174, Working Papers from New Economic School (NES) 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. Keywords: Incomplete preference relations; Expected Utility; Nash Equilibrium; Nonbinary Choice; Social Planning; Incomplete Knowledge (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:abo:neswpt:w0174 Access Statistics for this paper More papers in Working Papers from New Economic School (NES) Contact information at EDIRC. |
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