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Two Characterizations of Consistency

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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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File URL: http://economics.uwo.ca/research/department_working_papers_docs/wp2005/wp2005_2.pdf
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Bibliographic Info

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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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. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-94, July.
  2. Roger B. Myerson, 1984. "Multistage Games with Communication," Discussion Papers 590, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Choice under Uncertainty," Econometrica, Econometric Society, vol. 59(1), pages 61-79, January.
  4. Srihari Govindan & Tilman Klumpp, 2003. "Perfect equilibrium and lexicographic beliefs," International Journal of Game Theory, Springer, vol. 31(2), pages 229-243.
  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.
  6. McLennan, Andrew, 1989. "The Space of Conditional Systems is a Ball," International Journal of Game Theory, Springer, vol. 18(2), pages 125-39.
  7. 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.
  8. Vieille, Nicolas, 1996. "Conditional Systems Revisited," International Journal of Game Theory, Springer, vol. 25(2), pages 207-17.
  9. 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.
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Cited by:
  1. 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.

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