Two Characterizations of Consistency

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Two Characterizations of Consistency

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Peter A. Streufert (University of Western Ontario)

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Peter Alfred Streufert

Abstract

This paper offers two characterizations of the Kreps-Wilson concept of consistent beliefs. One is primarily of applied interest: beliefs are consistent iff they can be constructed by multiplying together vectors of monomials which induce the strategies. The other is primarily of conceptual interest: beliefs are consistent iff they can be induced by a "product dispersion" whose marginal dispersions induce the strategies (a "dispersion" is defined as a relative probability system, and a "product" dispersion is defined as a joint dispersion whose marginal dispersions are independent). Both these characterizations are derived with linear algebra.

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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 20052.

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Date of creation: 2005
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Handle: RePEc:uwo:uwowop:20052

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NEP-ALL-2005-10-22 (All new papers)

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

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.
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. [Downloadable!] (restricted)
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. [Downloadable!]
Other versions:
- 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. [Downloadable!]
McLennan, Andrew, 1989. "The Space of Conditional Systems is a Ball," International Journal of Game Theory, Springer, vol. 18(2), pages 125-39.
Vieille, Nicolas, 1996. "Conditional Systems Revisited," International Journal of Game Theory, Springer, vol. 25(2), pages 207-17.
Myerson, Roger B, 1986. "Multistage Games with Communication," Econometrica, Econometric Society, vol. 54(2), pages 323-58, March. [Downloadable!] (restricted)
Other versions:
- Roger B. Myerson, 1984. "Multistage Games with Communication," Discussion Papers 590, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Choice under Uncertainty," Econometrica, Econometric Society, vol. 59(1), pages 61-79, January. [Downloadable!] (restricted)
Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-94, July. [Downloadable!] (restricted)
Other versions:
- David M Kreps & Robert Wilson, 2003. "Sequential Equilibrium," Levine's Working Paper Archive 618897000000000813, David K. Levine. [Downloadable!]

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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. [Downloadable!]

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