Nonstandard utilities and the foundation of game theory

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.