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Published December 1, 2008 | Accepted Version
Journal Article Open

Ordinal notions of submodularity


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.

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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Accepted Version - CHAjme08preprint.pdf


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