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A space of lexicographic preferences

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  • Lee, Byung Soo

Abstract

There are many lexicographic probability systems (LPS’s) that represent the same lexicographic expected utility (LEU) preference relation (Blume et al., 1991). The space of all LPS’s on a Polish space therefore contains redundant representations of preferences. We show that there exists a Polish subspace of LPS’s that represents all LEU preference relations without such redundancies. Our approach is novel in that it frames the question as what is called a Borel section problem in classical descriptive set theory. The results are motivated by conceptual issues relevant to applications in epistemic game theory.

Suggested Citation

  • Lee, Byung Soo, 2016. "A space of lexicographic preferences," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 16-25.
    • Handle: RePEc:eee:mateco:v:65:y:2016:i:c:p:16-25
    DOI: 10.1016/j.jmateco.2016.04.005
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    References listed on IDEAS

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    1. Liu, Qingmin, 2009. "On redundant types and Bayesian formulation of incomplete information," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2115-2145, September.
    2. Keisler, H. Jerome & Lee, Byung Soo, 2011. "Common assumption of rationality," MPRA Paper 34441, University Library of Munich, Germany.
    3. Epstein, Larry G & Wang, Tan, 1996. ""Beliefs about Beliefs" without Probabilities," Econometrica, Econometric Society, vol. 64(6), pages 1343-1373, November.
    4. Lawrence Blume & Adam Brandenburger & Eddie Dekel, 2014. "Lexicographic Probabilities and Choice Under Uncertainty," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 6, pages 137-160, World Scientific Publishing Co. Pte. Ltd..
    5. ,, 2008. "Subjective expected utility in games," Theoretical Economics, Econometric Society, vol. 3(3), September.
    6. Yang, Chih-Chun, 2015. "Weak assumption and iterative admissibility," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 87-101.
    7. Adam Brandenburger & Amanda Friedenberg & H. Jerome Keisler, 2014. "Admissibility in Games," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 7, pages 161-212, World Scientific Publishing Co. Pte. Ltd..
    8. Lee, Byung Soo, 2016. "Admissibility and assumption," Journal of Economic Theory, Elsevier, vol. 163(C), pages 42-72.
    9. Lee, Byung Soo, 2013. "Conditional Beliefs and Higher-Order Preferences," MPRA Paper 48551, University Library of Munich, Germany.
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