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Utility representation of an incomplete and nontransitive preference relation

Hiroki Nishimura and Efe Ok

Journal of Economic Theory, 2016, vol. 166, issue C, pages 164-185

Abstract: 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.

Keywords: Nontransitive binary relations; Continuous utility; Debreu's theorem; Multi-utility representation (search for similar items in EconPapers)
JEL-codes: D11 D81 (search for similar items in EconPapers)
Date: 2016
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