Ordinal notions of submodularity
AbstractWe 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 InfoArticle provided by Elsevier in its journal Journal of Mathematical Economics.
Volume (Year): 44 (2008)
Issue (Month): 11 (December)
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Web page: http://www.elsevier.com/locate/jmateco
Quasisupermodularity Quasisubmodularity Comparative statics Submodularity;
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- Milgrom, P. & Shannon, C., 1991.
"Monotone Comparative Statics,"
11, Stanford - Institute for Thoretical Economics.
- Larry G. Epstein & Massimo Marinacci, 2006.
"Mutual Absolute Continuity of Multiple Priors,"
Carlo Alberto Notebooks
19, Collegio Carlo Alberto.
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