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Lexicographic probability, conditional probability, and nonstandard probability

Name: Lexicographic probability, conditional probability, and nonstandard probability
Creator: Joseph Y. Halpern
Keywords: FOS: Computer and information sciences, I.2.3, Artificial Intelligence (cs.AI), Computer Science - Computer Science and Game Theory, Computer Science - Artificial Intelligence, 0502 economics and business, 05 social sciences, 06 humanities and the arts, 0603 philosophy, ethics and religion, Computer Science and Game Theory (cs.GT)

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2010Embargo end date: 01 Jan 2003 English Publisher:Elsevier BVJournal:Games and Economic Behavior, volume 68, pages 155-179 (issn: 0899-8256,

Authors: Joseph Y. Halpern;

doi: 10.1016/j.geb.2009.03.013 , 10.48550/arxiv.cs/0306106

arXiv: http://arxiv.org/abs/cs/0306106

Lexicographic probability, conditional probability, and nonstandard probability

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Abstract

The relationship between Popper spaces (conditional probability spaces that satisfy some regularity conditions), lexicographic probability systems (LPS's), and nonstandard probability spaces (NPS's) is considered. If countable additivity is assumed, Popper spaces and a subclass of LPS's are equivalent; without the assumption of countable additivity, the equivalence no longer holds. If the state space is finite, LPS's are equivalent to NPS's. However, if the state space is infinite, NPS's are shown to be more general than LPS's.

A preliminary version appears in Proceedings of the Eighth Conference on Theoretical Aspects of Rationality and Knowledge, 2001, pp. 17--30. The final version will appear in Games and Economic Behavior

Related Organizations

Cornell University
United States

Keywords

FOS: Computer and information sciences, I.2.3, Artificial Intelligence (cs.AI), Computer Science - Computer Science and Game Theory, Computer Science - Artificial Intelligence, Computer Science and Game Theory (cs.GT)

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