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Infinite supermodularity and preferences

Author

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  • Alain Chateauneuf

    (IPAG Business School, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Vassili Vergopoulos

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Jianbo Zhang

    (Department of economics, University of Kansas - KU - University of Kansas [Lawrence])

Abstract

Chambers and Echenique (J Econ Theory 144:1004–1014, 2009) proved that preferences in a wide class cannot disentangle the usual economic assumptions of quasisupermodularity and supermodularity. This paper further studies the ordinal content of the much stronger assumption of infinite supermodularity in the same context. It is shown that weakly increasing binary relations on finite lattices fail to disentangle infinite supermodularity from quasisupermodularity and supermodularity. Moreover, for a complete preorder, the mild requirement of strict increasingness is shown to imply the existence of infinitely supermodular representations.

Suggested Citation

  • Alain Chateauneuf & Vassili Vergopoulos & Jianbo Zhang, 2016. "Infinite supermodularity and preferences," PSE-Ecole d'économie de Paris (Postprint) hal-01302555, HAL.
    • Handle: RePEc:hal:pseptp:hal-01302555
    DOI: 10.1007/s00199-015-0942-3
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    References listed on IDEAS

    as
    1. Klaus Nehring & Clemens Puppe, 2002. "A Theory of Diversity," Econometrica, Econometric Society, vol. 70(3), pages 1155-1198, May.
    2. Chateauneuf, Alain & Jaffray, Jean-Yves, 1989. "Some characterizations of lower probabilities and other monotone capacities through the use of Mobius inversion," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 263-283, June.
    3. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    4. Chambers, Christopher P. & Echenique, Federico, 2008. "Ordinal notions of submodularity," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1243-1245, December.
    5. Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, vol. 47(3), pages 565-577, May.
    6. Chambers, Christopher P. & Echenique, Federico, 2009. "Supermodularity and preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1004-1014, May.
    7. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
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    Cited by:

    1. Brian Duricy, 2023. "Preferences on Ranked-Choice Ballots," Papers 2301.02697, arXiv.org.

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    More about this item

    Keywords

    Supermodularity; Infinite supermodularity; Lattice;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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