Non-Archimedean Subjective Probabilities in Decision Theory and Games

Peter Hammond

Working Papers from Stanford University, Department of Economics

Abstract: December 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.

Keywords: Non-Archimedean probabilities; subjective expected utility; Anscombe--Aumann axioms; lexicographic expected utility; conditional probability systems; reduction of compound lotteries (search for similar items in EconPapers)
Date: 1997-12-07
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Journal Article: Non-Archimedean subjective probabilities in decision theory and games (1999)
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