Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
972318 | Mathematical Social Sciences | 2008 | 6 Pages |
Topological separability is crucial for the utility representation of a complete preference relation. When preferences are incomplete, this axiom has suitably defined counterparts: Upper separability and lower separability [Ok, E.A., 2002. Utility representation of an incomplete preference relation. Journal of Economic Theory 104, 429–449]. We consider the problem of representing an incomplete preference relation by means of a vector-valued utility function; we obtain representation results under the lower separability assumption. Our results extend the main representation theorems by Ok [Ok, E.A., 2002. Utility representation of an incomplete preference relation. Journal of Economic Theory 104, 429–449] in terms of the separability axioms.