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Products of Several Relative Probabilities

This paper defines and develops the concept of a product dispersion over any finite number of dimensions. The concept itself is nontrivial because products over several dimensions cannot be constructed by an iterative binary operation. Yet the paper's most important contribution is to characterize product dispersions by means of monomials. This result is derived through elementary linear algebra, and can be used to characterize the consistency of beliefs in extensive-form games (Streufert (2006a)).

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File URL: http://economics.uwo.ca/research/department_working_papers_docs/wp2006/wp2006_1.pdf
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Paper provided by University of Western Ontario, Department of Economics in its series UWO Department of Economics Working Papers with number 20061.

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Date of creation: 2006
Date of revision:
Handle: RePEc:uwo:uwowop:20061
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

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  1. 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..
  2. Peter A. Streufert, 2006. "Characterizing Consistency by Monomials and by Product Dispersions," UWO Department of Economics Working Papers 20062, University of Western Ontario, Department of Economics.
  3. David M Kreps & Robert Wilson, 2003. "Sequential Equilibria," Levine's Working Paper Archive 618897000000000813, David K. Levine.
  4. Peter A. Streufert, 2004. "Products of Representations Characterize the Products of Dispersions and the Consistency of Beliefs," Econometric Society 2004 North American Summer Meetings 548, Econometric Society.
  5. Myerson, Roger B, 1986. "Multistage Games with Communication," Econometrica, Econometric Society, vol. 54(2), pages 323-58, March.
  6. McLennan, Andrew, 1989. "The Space of Conditional Systems is a Ball," International Journal of Game Theory, Springer, vol. 18(2), pages 125-39.
  7. Vieille, Nicolas, 1996. "Conditional Systems Revisited," International Journal of Game Theory, Springer, vol. 25(2), pages 207-17.
  8. 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.
  9. Monderer, Dov & Samet, Dov & Shapley, Lloyd S, 1992. "Weighted Values and the Core," International Journal of Game Theory, Springer, vol. 21(1), pages 27-39.
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