Nonstandard utilities and the foundation of game theory

H. J. Skala

doi:10.1007/BF01766393

International Journal of Game Theory

June 1974, Volume 3, Issue 2, pp 67–81

Nonstandard utilities and the foundation of game theory

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H. J. Skala

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Received:: 15 December 1972
Revised:: 15 November 1973

DOI: 10.1007/BF01766393

Cite this article as:: Skala, H.J. Int J Game Theory (1974) 3: 67. doi:10.1007/BF01766393

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Abstract

In a recent paperFishburn [1972] discussed some consequences which the use of non-Archimedean utilities has on finite two-person zero-sum games. We shall show that the state of affairs with non-Archimedean utilities is not so different from the results undervon Neumann-Morgenstern utilities asFishburn asserts, if we represent the utilities in an appropriate non-Archimedean ordered field (nonstandard model of the real numbers) and admit that the components of the optimal strategies also may assume values in this ordered field. Moreover it is proved that for every utility space (in the sense ofHausner [1954] a nonstandard utility function exists.

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H. J. Skala
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1.Alfred-Weber-Institut für Sozial- und Staatswissenschaften der Universität HeidelbergHeidelberg

Nonstandard utilities and the foundation of game theory

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