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Products of Several Relative Probabilities

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Abstract

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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Bibliographic Info

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
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Handle: RePEc:uwo:uwowop:20061

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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. Vieille, Nicolas, 1996. "Conditional Systems Revisited," International Journal of Game Theory, Springer, vol. 25(2), pages 207-17.
  2. McLennan, Andrew, 1989. "The Space of Conditional Systems is a Ball," International Journal of Game Theory, Springer, vol. 18(2), pages 125-39.
  3. 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.
  4. 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.
  5. Peter A. Streufert, 2003. "Products of Representations Characterize the Products of Dispersions and the Consistency of Beliefs," UWO Department of Economics Working Papers 20039, University of Western Ontario, Department of Economics.
  6. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-94, July.
  7. 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.
  8. Myerson, Roger B, 1986. "Multistage Games with Communication," Econometrica, Econometric Society, vol. 54(2), pages 323-58, March.
  9. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Choice under Uncertainty," Econometrica, Econometric Society, vol. 59(1), pages 61-79, January.
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