Scalarization methods and expected multi-utility representations

• 成果类型: Article
• 署名作者: Evren, Oezguer
• 署名单位: New Economic School
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2014.02.003
• 发表日期: 2014
• 页码: 30-63
• 关键词: Incomplete preferences; expected utility; Nash equilibrium; Nonbinary choice; Maxmin under risk; Pareto efficiency

摘要

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. (C) 2014 Elsevier Inc. All rights reserved.