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Utility representation of an incomplete and nontransitive preference relation

Listed author(s):
  • Nishimura, Hiroki
  • Ok, Efe A.

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.

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File URL: http://www.sciencedirect.com/science/article/pii/S0022053116300448
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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 166 (2016)
Issue (Month): C ()
Pages: 164-185

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Handle: RePEc:eee:jetheo:v:166:y:2016:i:c:p:164-185
DOI: 10.1016/j.jet.2016.07.002
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Paola Manzini & Marco Mariotti, 2007. "Sequentially Rationalizable Choice," American Economic Review, American Economic Association, vol. 97(5), pages 1824-1839, December.
  2. Ok, Efe A., 2002. "Utility Representation of an Incomplete Preference Relation," Journal of Economic Theory, Elsevier, vol. 104(2), pages 429-449, June.
  3. Hiroki Nishimura & Efe A. Ok & John K.-H. Quah, 2017. "A Comprehensive Approach to Revealed Preference Theory," American Economic Review, American Economic Association, vol. 107(4), pages 1239-1263, April.
  4. Arouri, Mohamed & Teulon, Frédéric & Rault, Christophe, 2013. "Equity risk premium and regional integration," International Review of Financial Analysis, Elsevier, vol. 28(C), pages 79-85.
  5. Sondermann, Dieter, 1980. "Utility representations for partial orders," Journal of Economic Theory, Elsevier, vol. 23(2), pages 183-188, October.
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  8. Yusufcan Masatlioglu & Efe A. Ok, 2014. "A Canonical Model of Choice with Initial Endowments," Review of Economic Studies, Oxford University Press, vol. 81(2), pages 851-883.
  9. Wei He & Nicholas C. Yannelis, 2013. "A New Perspective on Rational Expectations," The School of Economics Discussion Paper Series 1317, Economics, The University of Manchester.
  10. ., 2013. "The corporation as a political actor," Chapters,in: The Political Power of the Business Corporation, chapter 2, pages 21-41 Edward Elgar Publishing.
  11. Shafer, Wayne J, 1974. "The Nontransitive Consumer," Econometrica, Econometric Society, vol. 42(5), pages 913-919, September.
  12. ., 2013. "Industrial policy of the Obama administration," Chapters,in: Industrial Policy in America, chapter 5, pages 96-102 Edward Elgar Publishing.
  13. Ok, Efe A. & Masatlioglu, Yusufcan, 2007. "A theory of (relative) discounting," Journal of Economic Theory, Elsevier, vol. 137(1), pages 214-245, November.
  14. Bosi, Gianni & Herden, Gerhard, 2012. "Continuous multi-utility representations of preorders," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 212-218.
  15. Lehrer, Ehud & Teper, Roee, 2011. "Justifiable preferences," Journal of Economic Theory, Elsevier, vol. 146(2), pages 762-774, March.
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  18. Eliaz, Kfir & Ok, Efe A., 2006. "Indifference or indecisiveness? Choice-theoretic foundations of incomplete preferences," Games and Economic Behavior, Elsevier, vol. 56(1), pages 61-86, July.
  19. ., 2013. "Haavelmo reconsidered as rational econometric man," Chapters,in: Rational Econometric Man, chapter 2, pages 35-60 Edward Elgar Publishing.
  20. Evren, Özgür & Ok, Efe A., 2011. "On the multi-utility representation of preference relations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 554-563.
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