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Ordinal notions of submodularity


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  • Chambers, Christopher P.
  • Echenique, Federico


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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 44 (2008)
Issue (Month): 11 (December)
Pages: 1243-1245

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Handle: RePEc:eee:mateco:v:44:y:2008:i:11:p:1243-1245

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Keywords: Quasisupermodularity Quasisubmodularity Comparative statics Submodularity;


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  1. Larry G. Epstein & Massimo Marinacci, 2006. "Mutual Absolute Continuity of Multiple Priors," Carlo Alberto Notebooks, Collegio Carlo Alberto 19, Collegio Carlo Alberto.
  2. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers, Stanford - Institute for Thoretical Economics 11, Stanford - Institute for Thoretical Economics.
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