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Supermodularity and preferences

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  • Chambers, Christopher P.
  • Echenique, Federico

Abstract

We uncover the complete ordinal implications of supermodularity on finite lattices under the assumption of weak monotonicity. In this environment, we show that supermodularity is ordinally equivalent to the notion of quasisupermodularity introduced by Milgrom and Shannon. We conclude that supermodularity is a weak property, in the sense that many preferences have a supermodular representation.

Suggested Citation

  • Chambers, Christopher P. & Echenique, Federico, 2009. "Supermodularity and preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1004-1014, May.
  • Handle: RePEc:eee:jetheo:v:144:y:2009:i:3:p:1004-1014
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    References listed on IDEAS

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    1. George J. Stigler, 1950. "The Development of Utility Theory. II," Journal of Political Economy, University of Chicago Press, vol. 58, pages 373-373.
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    8. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    9. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
    10. Matzkin, Rosa L, 1991. "Axioms of Revealed Preference for Nonlinear Choice Sets," Econometrica, Econometric Society, vol. 59(6), pages 1779-1786, November.
    11. Yakar Kannai, 2005. "Remarks concerning concave utility functions on finite sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 333-344, August.
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    Citations

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    Cited by:

    1. 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.
    2. Ennio Bilancini, 2010. "On the Rationalizability of Observed Consumers Choise when Prefeerences else," Department of Economics 0636, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".
    3. Ennio Bilancini, 2011. "On the rationalizability of observed consumers’ choices when preferences depend on budget sets and (potentially) on anything else," Journal of Economics, Springer, vol. 102(3), pages 275-286, April.
    4. Chambers, Christopher P. & Echenique, Federico, 2008. "Ordinal notions of submodularity," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1243-1245, December.
    5. Chambers, Christopher P. & Echenique, Federico & Shmaya, Eran, 2010. "On behavioral complementarity and its implications," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2332-2355, November.
    6. Forges, Françoise & Iehlé, Vincent, 2014. "Afriat’s theorem for indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 1-6.
    7. Julia Bachtrögler & Harald Badinger & Aurélien Fichet de Clairfontaine & Wolf Heinrich Reuter, 2014. "Summarizing Data using Partially Ordered Set Theory: An Application to Fiscal Frameworks in 97 Countries," Department of Economics Working Papers wuwp181, Vienna University of Economics and Business, Department of Economics.
    8. repec:hal:wpaper:halshs-00870052 is not listed on IDEAS
    9. Kalandrakis, Tasos, 2010. "Rationalizable voting," Theoretical Economics, Econometric Society, vol. 5(1), January.
    10. Hatfield, John William & Kominers, Scott Duke, 2017. "Contract design and stability in many-to-many matching," Games and Economic Behavior, Elsevier, vol. 101(C), pages 78-97.
    11. Francetich, Alejandro, 2013. "Notes on supermodularity and increasing differences in expected utility," Economics Letters, Elsevier, vol. 121(2), pages 206-209.
    12. Andrés Carvajal, 2010. "The testable implications of competitive equilibrium in economies with externalities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 349-378, October.
    13. Hatfield, John William & Kominers, Scott Duke, 2010. "Matching Networks with Bilateral Contracts," Research Papers 2050, Stanford University, Graduate School of Business.
    14. Alain Chateauneuf & Vassili Vergopoulos & Jianbo Zhang, 2017. "Infinite supermodularity and preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 99-109, January.
    15. Badinger, Harald & Reuter, Wolf Heinrich, 2015. "Measurement of fiscal rules: Introducing the application of partially ordered set (POSET) theory," Journal of Macroeconomics, Elsevier, vol. 43(C), pages 108-123.

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