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Lexicographic probability, conditional probability, and nonstandard probability

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  • Halpern, Joseph Y.

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.

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  • Halpern, Joseph Y., 2010. "Lexicographic probability, conditional probability, and nonstandard probability," Games and Economic Behavior, Elsevier, vol. 68(1), pages 155-179, January.
  • Handle: RePEc:eee:gamebe:v:68:y:2010:i:1:p:155-179
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    Cited by:

    1. Di Tillio, Alfredo & Halpern, Joseph Y. & Samet, Dov, 2014. "Conditional belief types," Games and Economic Behavior, Elsevier, pages 253-268.
    2. Tsakas, Elias, 2014. "Epistemic equivalence of extended belief hierarchies," Games and Economic Behavior, Elsevier, pages 126-144.
    3. Streufert, Peter A., 2015. "An elementary proof that additive i-likelihood characterizes the supports of consistent assessments," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 37-46.
    4. Marcus Pivato, 2014. "Additive representation of separable preferences over infinite products," Theory and Decision, Springer, pages 31-83.
    5. Lee, Byung Soo, 2013. "Conditional Beliefs and Higher-Order Preferences," MPRA Paper 48551, University Library of Munich, Germany.
    6. Marcus Pivato, 2014. "Additive representation of separable preferences over infinite products," Theory and Decision, Springer, pages 31-83.
    7. Asheim, Geir B. & Perea, Andres, 2005. "Sequential and quasi-perfect rationalizability in extensive games," Games and Economic Behavior, Elsevier, pages 15-42.
    8. Peter A. Streufert, 2012. "Additive Plausibility Characterizes the Supports of Consistent Assessments," UWO Department of Economics Working Papers 20123, University of Western Ontario, Department of Economics.
    9. repec:spr:jogath:v:46:y:2017:i:2:d:10.1007_s00182-016-0535-9 is not listed on IDEAS

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