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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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 144 (2009)
Issue (Month): 3 (May)
Pages: 1004-1014

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Handle: RePEc:eee:jetheo:v:144:y:2009:i:3:p:1004-1014

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Web page: http://www.elsevier.com/locate/inca/622869

Related research

Keywords: Complementarity Revealed preference Afriat's theorem Refutability;

References

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  1. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  2. John K.-H Quah, 2007. "The Comparative Statics of Constrained Optimization Problems," Econometrica, Econometric Society, vol. 75(2), pages 401-431, 03.
  3. Chiappori, Pierre-Andre & Rochet, Jean-Charles, 1987. "Revealed Preferences and Differentiable Demand: Notes and Comments," Econometrica, Econometric Society, vol. 55(3), pages 687-91, May.
  4. Richter, Marcel K. & Wong, K.-C.Kam-Chau, 2004. "Concave utility on finite sets," Journal of Economic Theory, Elsevier, vol. 115(2), pages 341-357, April.
  5. Matzkin, Rosa L, 1991. "Axioms of Revealed Preference for Nonlinear Choice Sets," Econometrica, Econometric Society, vol. 59(6), pages 1779-86, November.
  6. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
  7. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  8. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  9. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  10. George J. Stigler, 1950. "The Development of Utility Theory. I," Journal of Political Economy, University of Chicago Press, vol. 58, pages 307.
  11. Yakar Kannai, 2005. "Remarks concerning concave utility functions on finite sets," Economic Theory, Springer, vol. 26(2), pages 333-344, 08.
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Citations

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Cited by:
  1. 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.
  2. Francoise Forges & Vincent Iehlé, 2014. "Afriat's theorem for indivisible goods," Working Papers halshs-00870052, HAL.
  3. Ennio Bilancini, 2010. "On the rationalizability of observed consumers’ choices when preferences depend on budget sets and (potentially) on anything else," Center for Economic Research (RECent) 052, University of Modena and Reggio E., Dept. of Economics.
  4. Hatfield, John William & Kominers, Scott Duke, 2010. "Matching Networks with Bilateral Contracts," Research Papers 2050, Stanford University, Graduate School of Business.
  5. Andrés Carvajal, 2010. "The testable implications of competitive equilibrium in economies with externalities," Economic Theory, Springer, vol. 45(1), pages 349-378, October.
  6. Kalandrakis, Tasos, 2010. "Rationalizable voting," Theoretical Economics, Econometric Society, vol. 5(1), January.
  7. Francetich, Alejandro, 2013. "Notes on supermodularity and increasing differences in expected utility," Economics Letters, Elsevier, vol. 121(2), pages 206-209.
  8. 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".

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