Representations of preorders by strong multi-objective functions
AbstractWe introduce a new kind of representation of a not necessarily total preorder, called strong multi-utility representation, according to which not only the preorder itself but also its strict part is fully represented by a family of multi-objective functions. The representability by means of semicontinuous or continuous multi-objective functions is discussed, as well as the relation between the existence of a strong multi-utility representation and the existence of a Richter-Peleg utility function. We further present conditions for the existence of a semicontinuous or continuous countable strong multi-utility representation.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 52329.
Date of creation: 01 Dec 2013
Date of revision:
Multi-utility representation; Richter-Peleg utility; Strong multi-utility;
Find related papers by JEL classification:
- C0 - Mathematical and Quantitative Methods - - General
- D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-12-29 (All new papers)
- NEP-MIC-2013-12-29 (Microeconomics)
- NEP-UPT-2013-12-29 (Utility Models & Prospect Theory)
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- Ok, Efe A., 2002. "Utility Representation of an Incomplete Preference Relation," Journal of Economic Theory, Elsevier, Elsevier, vol. 104(2), pages 429-449, June.
- Juan Dubra & Fabio Maccheroni & Efe Oki, 2001.
"Expected utility theory without the completeness axiom,"
ICER Working Papers - Applied Mathematics Series, ICER - International Centre for Economic Research
11-2001, ICER - International Centre for Economic Research.
- Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004. "Expected utility theory without the completeness axiom," Journal of Economic Theory, Elsevier, Elsevier, vol. 115(1), pages 118-133, March.
- Juan Dubra & Fabio Maacheroni & Efe A. Ok, 2001. "Expected Utility Theory without the Completeness Axiom," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1294, Cowles Foundation for Research in Economics, Yale University.
- Bosi, Gianni & Herden, Gerhard, 2012. "Continuous multi-utility representations of preorders," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 212-218.
- Bergstrom, Theodore C., 1975. "Maximal elements of acyclic relations on compact sets," Journal of Economic Theory, Elsevier, Elsevier, vol. 10(3), pages 403-404, June.
- Herden, Gerhard & Levin, Vladimir L., 2012. "Utility representation theorems for Debreu separable preorders," Journal of Mathematical Economics, Elsevier, vol. 48(3), pages 148-154.
- Kaminski, B., 2007. "On quasi-orderings and multi-objective functions," European Journal of Operational Research, Elsevier, Elsevier, vol. 177(3), pages 1591-1598, March.
- Evren, Özgür & Ok, Efe A., 2011. "On the multi-utility representation of preference relations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 554-563.
- Herden, Gerhard & Pallack, Andreas, 2002. "On the continuous analogue of the Szpilrajn Theorem I," Mathematical Social Sciences, Elsevier, Elsevier, vol. 43(2), pages 115-134, March.
- Schmeidler, David, 1971.
"A Condition for the Completeness of Partial Preference Relations,"
Econometrica, Econometric Society,
Econometric Society, vol. 39(2), pages 403-04, March.
- SCHMEIDLER, David, . "A condition for the completeness of partial preference relations," CORE Discussion Papers RP, UniversitÃ© catholique de Louvain, Center for Operations Research and Econometrics (CORE) -86, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Bosi, Gianni & Caterino, Alessandro & Ceppitelli, Rita, 2009. "Existence of continuous utility functions for arbitrary binary relations: some sufficient conditions," MPRA Paper 14808, University Library of Munich, Germany.
- Peleg, Bezalel, 1970. "Utility Functions for Partially Ordered Topological Spaces," Econometrica, Econometric Society, Econometric Society, vol. 38(1), pages 93-96, January.
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