Ordinal notions of submodularity

Christopher Chambers and Federico Echenique

Journal of Mathematical Economics, 2008, vol. 44, issue 11, 1243-1245

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.

Keywords: Quasisupermodularity; Quasisubmodularity; Comparative; statics; Submodularity (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:44:y:2008:i:11:p:1243-1245

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