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Representations of preorders by strong multi-objective functions

Author

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  • Alcantud, José Carlos R.
  • Bosi, Gianni
  • Zuanon, Magalì

Abstract

We 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.

Suggested Citation

  • Alcantud, José Carlos R. & Bosi, Gianni & Zuanon, Magalì, 2013. "Representations of preorders by strong multi-objective functions," MPRA Paper 52329, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:52329
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    File URL: https://mpra.ub.uni-muenchen.de/52329/1/MPRA_paper_52329.pdf
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    References listed on IDEAS

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    1. Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004. "Expected utility theory without the completeness axiom," Journal of Economic Theory, Elsevier, vol. 115(1), pages 118-133, March.
    2. Schmeidler, David, 1971. "A Condition for the Completeness of Partial Preference Relations," Econometrica, Econometric Society, vol. 39(2), pages 403-404, March.
    3. Herden, Gerhard & Levin, Vladimir L., 2012. "Utility representation theorems for Debreu separable preorders," Journal of Mathematical Economics, Elsevier, vol. 48(3), pages 148-154.
    4. Bosi, Gianni & Herden, Gerhard, 2012. "Continuous multi-utility representations of preorders," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 212-218.
    5. Herden, Gerhard & Pallack, Andreas, 2002. "On the continuous analogue of the Szpilrajn Theorem I," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 115-134, March.
    6. Ok, Efe A., 2002. "Utility Representation of an Incomplete Preference Relation," Journal of Economic Theory, Elsevier, vol. 104(2), pages 429-449, June.
    7. Peleg, Bezalel, 1970. "Utility Functions for Partially Ordered Topological Spaces," Econometrica, Econometric Society, vol. 38(1), pages 93-96, January.
    8. Kaminski, B., 2007. "On quasi-orderings and multi-objective functions," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1591-1598, March.
    9. Bergstrom, Theodore C., 1975. "Maximal elements of acyclic relations on compact sets," Journal of Economic Theory, Elsevier, vol. 10(3), pages 403-404, June.
    10. 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.
    11. 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.
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    Cited by:

    1. Alcantud, José Carlos R. & Dubey, Ram Sewak, 2014. "Ordering infinite utility streams: Efficiency, continuity, and no impatience," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 33-40.

    More about this item

    Keywords

    Multi-utility representation; Richter-Peleg utility; Strong multi-utility;

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles

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