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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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  • Peter A. Streufert, 2006. "Products of Several Relative Probabilities," UWO Department of Economics Working Papers 20061, University of Western Ontario, Department of Economics.
  • Handle: RePEc:uwo:uwowop:20061
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    1. 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.
    2. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    3. 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.
    4. W. M. Gorman, 1968. "The Structure of Utility Functions," Review of Economic Studies, Oxford University Press, vol. 35(4), pages 367-390.
    5. Vieille, Nicolas, 1996. "Conditional Systems Revisited," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(2), pages 207-217.
    6. 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..
    7. 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.
    8. Myerson, Roger B, 1986. "Multistage Games with Communication," Econometrica, Econometric Society, vol. 54(2), pages 323-358, March.
    9. 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.
    10. 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.
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