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Ordinal notions of submodularity

Chambers, Christopher P. and Echenique, Federico (2008) Ordinal notions of submodularity. Journal of Mathematical Economics, 44 (11). pp. 1243-1245. ISSN 0304-4068.

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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.

Item Type:Article
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URLURL TypeDescription
Chambers, Christopher P.0000-0001-8253-0328
Echenique, Federico0000-0002-1567-6770
Additional Information:Published version. Copyright © 2008 Elsevier. Received 16 July 2007; revised 11 March 2008; accepted 13 March 2008. Available online 21 March 2008. The authors would like to thank the National Science Foundation (SES-0751980) for financial support.
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Subject Keywords:Quasisupermodularity; Quasisubmodularity; Comparative statics; Submodularity
Issue or Number:11
Record Number:CaltechAUTHORS:CHAjme08
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:12416
Deposited By: Archive Administrator
Deposited On:25 Nov 2008 17:22
Last Modified:09 Mar 2020 13:18

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