Debreu-like properties of utility representations
Traditionally the codomain of a utility function is the set of real numbers. This choice has the advantage of ensuring the existence of a continuous representation but does not allow to represent many preference structures that are relevant to utility theory. Recently, some authors have started a systematic study of utility representations that are not real-valued, introducing the notion of a Debreu chain. We continue their analysis defining two Debreu-like properties, which are connected to a local continuity of a utility representation. The classes of locally Debreu and pointwise Debreu chains here introduced enlarge the class of Debreu chains. We give several examples and analyze some properties of these two classes of chains, with particular attention to lexicographic products.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Monteiro, Paulo Klinger, 1987. "Some results on the existence of utility functions on path connected spaces," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 147-156, April.
- Beardon, Alan F, 1994. "Utility Theory and Continuous Monotonic Functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(4), pages 531-538, May.
- Wakker, Peter, 1988. "Continuity of Preference Relations for Separable Topologies," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(1), pages 105-110, February.
- Herden, G. & Mehta, G. B., 2004. "The Debreu Gap Lemma and some generalizations," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 747-769, November.
- Beardon, Alan F. & Candeal, Juan C. & Herden, Gerhard & Indurain, Esteban & Mehta, Ghanshyam B., 2002. "Lexicographic decomposition of chains and the concept of a planar chain," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 95-104, April.
- Beardon, Alan F. & Candeal, Juan C. & Herden, Gerhard & Indurain, Esteban & Mehta, Ghanshyam B., 2002. "The non-existence of a utility function and the structure of non-representable preference relations," Journal of Mathematical Economics, Elsevier, vol. 37(1), pages 17-38, February.
- Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514-540, June.
- Candeal, Juan C. & Herves, Carlos & Indurain, Esteban, 1998. "Some results on representation and extension of preferences," Journal of Mathematical Economics, Elsevier, vol. 29(1), pages 75-81, January.
- Knoblauch, Vicki, 2000. "Lexicographic orders and preference representation," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 255-267, October.
- Campion, Maria J. & Candeal, Juan C. & Indurain, Esteban, 2006. "The existence of utility functions for weakly continuous preferences on a Banach space," Mathematical Social Sciences, Elsevier, vol. 51(2), pages 227-237, March.
When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:44:y:2008:i:11:p:1161-1179. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.