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Utility representation theorems for Debreu separable preorders

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  • Herden, Gerhard
  • Levin, Vladimir L.

Abstract

We prove the existence of arbitrary (resp., semicontinuous, continuous) utility representations for arbitrary (resp., semicontinuous, continuous) preorders satisfying some weakened Debreu order separability conditions. In this way we widely generalize a classical result for total preorders that essentially is due to Debreu.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 48 (2012)
Issue (Month): 3 ()
Pages: 148-154

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Handle: RePEc:eee:mateco:v:48:y:2012:i:3:p:148-154

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Web page: http://www.elsevier.com/locate/jmateco

Related research

Keywords: Debreu separability; Weak Debreu separability; Topological space; Continuous preorder; Utility function; Open decreasing set; Separable system;

References

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  1. Peleg, Bezalel, 1970. "Utility Functions for Partially Ordered Topological Spaces," Econometrica, Econometric Society, Econometric Society, vol. 38(1), pages 93-96, January.
  2. Alcantud, J. C. R. & Rodriguez-Palmero, C., 1999. "Characterization of the existence of semicontinuous weak utilities," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 32(4), pages 503-509, December.
  3. Herden, G., 1989. "On the existence of utility functions ii," Mathematical Social Sciences, Elsevier, Elsevier, vol. 18(2), pages 107-117, October.
  4. Itzhak Gilboa & Fabio Maccheroni & Massimo Marinacci & David Schmeidler, 2010. "Objective and Subjective Rationality in a Multiple Prior Model," Econometrica, Econometric Society, Econometric Society, vol. 78(2), pages 755-770, 03.
  5. Herden, G., 1989. "On the existence of utility functions," Mathematical Social Sciences, Elsevier, Elsevier, vol. 17(3), pages 297-313, June.
  6. 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.
  7. SCHMEIDLER, David, . "A condition for the completeness of partial preference relations," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -86, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. Mas-Colell, Andrew, 1974. "An equilibrium existence theorem without complete or transitive preferences," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 1(3), pages 237-246, December.
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Cited by:
  1. Giarlotta, Alfio & Greco, Salvatore, 2013. "Necessary and possible preference structures," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 49(2), pages 163-172.
  2. Bosi, Gianni & Zuanon, Magalì, 2014. "Upper semicontinuous representations of interval orders," Mathematical Social Sciences, Elsevier, Elsevier, vol. 68(C), pages 60-63.
  3. 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.

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