Lexicographic probability, conditional probability, and nonstandard probability
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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Joseph Y. Halpern, 2000.
"Characterizing the Common Prior Assumption,"
Game Theory and Information
- Stalnaker, Robert, 1998. "Belief revision in games: forward and backward induction1," Mathematical Social Sciences, Elsevier, vol. 36(1), pages 31-56, July.
- Adam Brandenburger & Amanda Friedenberg & H. Jerome Keisler, 2008. "Admissibility in Games," Econometrica, Econometric Society, vol. 76(2), pages 307-352, 03.
- Kreps, David M & Wilson, Robert, 1982.
Econometric Society, vol. 50(4), pages 863-94, July.
- Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January.
- Battigalli, Pierpaolo & Veronesi, Pietro, 1996. "A Note on Stochastic Independence without Savage-Null Events," Journal of Economic Theory, Elsevier, vol. 70(1), pages 235-248, July.
- Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
- Kohlberg, Elon & Reny, Philip J., 1997. "Independence on Relative Probability Spaces and Consistent Assessments in Game Trees," Journal of Economic Theory, Elsevier, vol. 75(2), pages 280-313, August.
- Asheim, Geir B. & Sovik, Ylva, 2005. "Preference-based belief operators," Mathematical Social Sciences, Elsevier, vol. 50(1), pages 61-82, July.
- Asheim, Geir B. & Perea, Andres, 2005. "Sequential and quasi-perfect rationalizability in extensive games," Games and Economic Behavior, Elsevier, vol. 53(1), pages 15-42, October.
- Myerson, Roger B, 1986.
"Multistage Games with Communication,"
Econometric Society, vol. 54(2), pages 323-58, March.
- Lawrence Blume & Adam Brandenburger & Eddie Dekel, 2014.
"Lexicographic Probabilities and Choice Under Uncertainty,"
World Scientific Book Chapters,
in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 6, pages 137-160
World Scientific Publishing Co. Pte. Ltd..
- Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Choice under Uncertainty," Econometrica, Econometric Society, vol. 59(1), pages 61-79, January.
- Battigalli, Pierpaolo & Siniscalchi, Marciano, 1999. "Interactive beliefs, epistemic independence and strong rationalizability," Research in Economics, Elsevier, vol. 53(3), pages 247-273, September.
- Fishburn, Peter C. & LaValle, Irving H., 1998. "Subjective expected lexicographic utility with infinite state sets," Journal of Mathematical Economics, Elsevier, vol. 30(3), pages 323-346, October.
When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:68:y:2010:i:1:p:155-179. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If references are entirely missing, you can add them using this form.