Non-Archimedean subjective probabilities in decision theory and games
AbstractDecember 7, 1997 To allow conditioning on counterfactual events, zero probabilities can be replaced by infinitesimal probabilities that range over a non-Archimedean ordered field. This paper considers a suitable minimal field that is a complete metric space. Axioms similar to those in Anscombe and Aumann (1963) and in Blume, Brandenburger and Dekel (1991) are used to characterize preferences which: (i) reveal unique non-Archimedean subjective probabilities within the field; and (ii) can be represented by the non-Archimedean subjective expected value of any real-valued von Neumann--Morgenstern utility function in a unique cardinal equivalence class, using the natural ordering of the field. Keywords: Non-Archimedean probabilities, subjective expected utility, Anscombe--Aumann axioms, lexicographic expected utility, conditional probability systems, reduction of compound lotteries.
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Bibliographic InfoArticle provided by Elsevier in its journal Mathematical Social Sciences.
Volume (Year): 38 (1999)
Issue (Month): 2 (September)
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Web page: http://www.elsevier.com/locate/inca/505565
Other versions of this item:
- Peter J. Hammond, 1997. "Non-Archimedean Subjective Probabilities in Decision Theory and Games," Working Papers 97038, Stanford University, Department of Economics.
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