Computer Science – Computer Science and Game Theory
Scientific paper
2003-06-17
Computer Science
Computer Science and Game Theory
A preliminary version appears in Proceedings of the Eighth Conference on Theoretical Aspects of Rationality and Knowledge, 200
Scientific paper
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.
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