Products of Representations Characterize the Products of Dispersions and the Consistency of Beliefs
A "dispersion" specifies the relative probability between any two elements of a finite domain. It thereby partitions the domain into equivalence classes separated by infinite relative probability. The paper's novelty is to numerically represent not only the order of the equivalence classes, but also the "magnitude" of the gaps between them. The paper's main theorem is that the many products of two dispersions are characterized algebraically by varying the magnitudes of the gaps between each factor's equivalence classes. An immediate corollary is that the many beliefs consistent with two strategies are characterized by varying each player's "steadiness" in avoiding various zero-probability options.
|Date of creation:||Jun 2003|
|Contact details of provider:|| Postal: Department of Economics, Reference Centre, Social Science Centre, University of Western Ontario, London, Ontario, Canada N6A 5C2|
Phone: 519-661-2111 Ext.85244
Web page: http://economics.uwo.ca/research/research_papers/department_working_papers.html
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.:
- Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
- Monderer, Dov & Samet, Dov & Shapley, Lloyd S, 1992. "Weighted Values and the Core," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(1), pages 27-39.
- 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.
- Myerson, Roger B, 1986. "Multistage Games with Communication," Econometrica, Econometric Society, vol. 54(2), pages 323-358, March.
- McLennan, Andrew, 1989. "The Space of Conditional Systems is a Ball," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(2), pages 125-139.
- 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.
- Kreps, David M & Ramey, Garey, 1987. "Structural Consistency, Consistency, and Sequential Rationality," Econometrica, Econometric Society, vol. 55(6), pages 1331-1348, November. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:uwo:uwowop:20039. 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: ()
If references are entirely missing, you can add them using this form.