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Products of Representations Characterize the Products of Dispersions and the Consistency of Beliefs

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  • Peter A. Streufert
Abstract
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

Suggested Citation

  • 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.
    • Handle: RePEc:ecm:nasm04:548
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    References listed on IDEAS

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    1. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    2. 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.
    3. 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..
    4. Myerson, Roger B, 1986. "Multistage Games with Communication," Econometrica, Econometric Society, vol. 54(2), pages 323-358, March.
    5. 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.
    6. 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.
    7. Kreps, David M & Ramey, Garey, 1987. "Structural Consistency, Consistency, and Sequential Rationality," Econometrica, Econometric Society, vol. 55(6), pages 1331-1348, November.
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    Cited by:

    1. Peter A. Streufert, 2005. "Two Characterizations of Consistency," University of Western Ontario, Departmental Research Report Series 20052, University of Western Ontario, Department of Economics.
    2. Peter A. Streufert, 2006. "Products of Several Relative Probabilities," University of Western Ontario, Departmental Research Report Series 20061, University of Western Ontario, Department of Economics.

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    More about this item

    Keywords

    consistent beliefs; relative probability;

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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