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Elementary non-Archimedean utility theory

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  • Herzberg, Frederik

Abstract

A non-Archimedean utility representation theorem for independent and transitive preference orderings that are partially continuous on some convex subset and satisfy an axiom of incommensurable preference for elements outside that subset is proven. For complete preference orderings, the theorem is deduced directly from the classical von Neumann-Morgenstern theorem; in the absence of completeness, Aumann's [Aumann, R.J., 1962. Utility theory without the completeness axiom. Econometrica 30 (3), 445-462] generalization is utilized.

Suggested Citation

  • Herzberg, Frederik, 2009. "Elementary non-Archimedean utility theory," Mathematical Social Sciences, Elsevier, vol. 58(1), pages 8-14, July.
    • Handle: RePEc:eee:matsoc:v:58:y:2009:i:1:p:8-14
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    References listed on IDEAS

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    1. Kannai, Yakar, 1992. "Non-standard concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 21(1), pages 51-58.
    2. Fishburn, Peter C. & Lavalle, Irving H., 1991. "Nonstandard nontransitive utility on mixture sets," Mathematical Social Sciences, Elsevier, vol. 21(3), pages 233-244, June.
    3. Lehmann, Daniel, 2001. "Expected Qualitative Utility Maximization," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 54-79, April.
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    Cited by:

    1. Werner Güth & Hartmut Kliemt, 2017. "How to Cope With (New) Uncertainties—A Bounded Rationality Approach," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 34(4), pages 343-359, December.
    2. Marcus Pivato, 2014. "Additive representation of separable preferences over infinite products," Theory and Decision, Springer, vol. 77(1), pages 31-83, June.
    3. David McCarthy & Kalle Mikkola & Teruji Thomas, 2019. "Aggregation for potentially infinite populations without continuity or completeness," Papers 1911.00872, arXiv.org.

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