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Infinite Supermodularity and Preferences

Author

Listed:
  • Alain Chateauneuf

    (IPAG Business School, Paris School of Economics and University of Paris I;)

  • Vassili Vergopoulos

    (Paris School of Economics and University of Paris I;)

  • Jianbo Zhang

    (Department of Economics, The University of Kansas;)

Abstract

Chambers and Echenique (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 nite lattices fail to disentangle in nite 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, 2015. "Infinite Supermodularity and Preferences," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201505, University of Kansas, Department of Economics, revised Oct 2015.
    • Handle: RePEc:kan:wpaper:201505
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    File URL: http://www2.ku.edu/~kuwpaper/2015Papers/201505.pdf
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    References listed on IDEAS

    as
    1. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    2. Chambers, Christopher P. & Echenique, Federico, 2008. "Ordinal notions of submodularity," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1243-1245, December.
    3. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    4. 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.
    5. Klaus Nehring & Clemens Puppe, 2002. "A Theory of Diversity," Econometrica, Econometric Society, vol. 70(3), pages 1155-1198, May.
    6. Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, vol. 47(3), pages 565-577, May.
    7. Chambers, Christopher P. & Echenique, Federico, 2009. "Supermodularity and preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1004-1014, 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:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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