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

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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.

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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 20039.

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Date of creation: Jun 2003
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Handle: RePEc:uwo:uwowop:20039

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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. 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.
  2. Myerson, Roger B, 1986. "Multistage Games with Communication," Econometrica, Econometric Society, vol. 54(2), pages 323-58, March.
  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. David Kreps & Robert Wilson, 1998. "Sequential Equilibria," Levine's Working Paper Archive 237, David K. Levine.
  5. McLennan, Andrew, 1989. "The Space of Conditional Systems is a Ball," International Journal of Game Theory, Springer, vol. 18(2), pages 125-39.
  6. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Choice under Uncertainty," Econometrica, Econometric Society, vol. 59(1), pages 61-79, January.
  7. Kreps, David M & Ramey, Garey, 1987. "Structural Consistency, Consistency, and Sequential Rationality," Econometrica, Econometric Society, vol. 55(6), pages 1331-48, November.
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Cited by:
  1. Peter A. Streufert, 2005. "Two Characterizations of Consistency," UWO Department of Economics Working Papers 20052, University of Western Ontario, Department of Economics.
  2. Peter A. Streufert, 2006. "Products of Several Relative Probabilities," UWO Department of Economics Working Papers 20061, University of Western Ontario, Department of Economics.

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