Utility representation of an incomplete and nontransitive preference relation

• 成果类型: Article
• 署名作者: Nishimura, Hiroki; Ok, Efe A.
• 署名单位: University of California System; University of California Riverside; New York University; New York University
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2016.07.002
• 发表日期: 2016
• 页码: 164-185
• 关键词: Nontransitive binary relations; Continuous utility; Debreu's theorem; Multi-utility representation

摘要

The objective of this paper is to provide continuous utility representation theorems analogous to Debreu's classic utility representation theorem, albeit for preference relations that may fail to be complete and/or transitive. Specifically, we show that every (continuous and) reflexive binary relation on a (compact) metric space can be represented by means of the maxmin, or dually, minmax, of a (compact) set of (compact) sets of continuous utility functions. This notion of maxmin multi-utility representation,generalizes the recently proposed notions of multi-utility representation for preorders and justifiable preferences for complete and quasitransitive relations. As such, our main representation theorems lead to some new characterizations of these special cases as well. (C) 2016 Published by Elsevier Inc.