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Characterizing Consistency by Monomials and by Product Dispersions

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Abstract

This paper derives two characterizations of the Kreps-Wilson concept of consistent beliefs. In the first, beliefs are shown to be consistent iff they can be constructed from the elements of monomial vectors which converge to the strategies. In the second, beliefs are shown to be consistent iff they can be induced by a product dispersion whose marginal dispersions induce the strategies. The first characterization is simpler than the definition in Kreps and Wilson (1982), and the second seems more fundamental in the sense that it is built on an underlying theory of relative probability.

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  • Peter A. Streufert, 2006. "Characterizing Consistency by Monomials and by Product Dispersions," University of Western Ontario, Departmental Research Report Series 20062, University of Western Ontario, Department of Economics.
    • Handle: RePEc:uwo:uwowop:20062
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    1. Fudenberg, Drew & Tirole, Jean, 1991. "Perfect Bayesian equilibrium and sequential equilibrium," Journal of Economic Theory, Elsevier, vol. 53(2), pages 236-260, April.
    2. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    3. Perea y Monsuwe, Andres & Jansen, Mathijs & Peters, Hans, 1997. "Characterization of Consistent Assessments in Extensive Form Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 238-252, October.
    4. Peter A. Streufert, 2005. "Two Characterizations of Consistency," University of Western Ontario, Departmental Research Report Series 20052, University of Western Ontario, Department of Economics.
    5. 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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    1. 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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