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Ordinal notions of submodularity

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  • Chambers, Christopher P.
  • Echenique, Federico

Abstract

We consider several ordinal formulations of submodularity, defined for arbitrary binary relations on lattices. Two of these formulations are essentially due to Kreps [Kreps, D.M., 1979. A representation theorem for "Preference for Flexibility". Econometrica 47 (3), 565-578] and one is a weakening of a notion due to Milgrom and Shannon [Milgrom, P., Shannon, C., 1994. Monotone comparative statics. Econometrica 62 (1), 157-180]. We show that any reflexive binary relation satisfying either of Kreps's definitions also satisfies Milgrom and Shannon's definition, and that any transitive and monotonic binary relation satisfying the Milgrom and Shannon's condition satisfies both of Kreps's conditions.

Suggested Citation

  • Chambers, Christopher P. & Echenique, Federico, 2008. "Ordinal notions of submodularity," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1243-1245, December.
    • Handle: RePEc:eee:mateco:v:44:y:2008:i:11:p:1243-1245
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    References listed on IDEAS

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    1. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    2. Epstein, Larry G. & Marinacci, Massimo, 2007. "Mutual absolute continuity of multiple priors," Journal of Economic Theory, Elsevier, vol. 137(1), pages 716-720, November.
    3. 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. Chambers, Christopher P. & Miller, Alan D. & Yenmez, M. Bumin, 2020. "Closure and preferences," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 161-166.
    2. Alain Chateauneuf & Vassili Vergopoulos & Jianbo Zhang, 2018. "Infinite Supermodularity and Preferences," Chapters, in: Danijela Tuljak-Suban (ed.), Game Theory - Applications in Logistics and Economy, IntechOpen.
    3. Brian Duricy, 2023. "Preferences on Ranked-Choice Ballots," Papers 2301.02697, arXiv.org.

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