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Weakly-Bayesian and Consistent Assessments

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  • Carlos Pimienta

    ()
    (School of Economics, The University of New South Wales)

Abstract

A weakly-Bayesian assessment is computed applying Bayes rule at positive probability information sets. We characterize the set of extensive-forms for which the sets of weakly-Bayesian and consistent assessments coincide. In doing so we disentangle the different restrictions imposed by consistency across information sets. We apply this knowledge to strengthen weakly-Bayesian assessments and to derive conditions for equivalence with consistency that can be useful in economic applications.

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File URL: http://research.economics.unsw.edu.au/RePEc/papers/2012-02.pdf
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Bibliographic Info

Paper provided by School of Economics, The University of New South Wales in its series Discussion Papers with number 2012-02.

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Length: 34 pages
Date of creation: Oct 2011
Date of revision:
Handle: RePEc:swe:wpaper:2012-02

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Keywords: Backwards induction; Weakly-Bayesian assessments; Consistent assessments; Sequential equilibrium; Extensive-forms.;

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References

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  1. Battigalli, Pierpaolo, 1996. "Strategic Independence and Perfect Bayesian Equilibria," Journal of Economic Theory, Elsevier, vol. 70(1), pages 201-234, July.
  2. 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.
  3. Perea, Andres, 2002. "A note on the one-deviation property in extensive form games," Games and Economic Behavior, Elsevier, vol. 40(2), pages 322-338, August.
  4. David Kreps & Robert Wilson, 1998. "Sequential Equilibria," Levine's Working Paper Archive 237, David K. Levine.
  5. Jeroen M. Swinkels, 1993. "Independence for Conditional Probability Systems," Discussion Papers 1076, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, September.
  7. 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.
  8. McLennan, Andrew, 1989. "Consistent Conditional Systems in Noncooperative Game Theory," International Journal of Game Theory, Springer, vol. 18(2), pages 141-74.
  9. Myerson, Roger B, 1986. "Multistage Games with Communication," Econometrica, Econometric Society, vol. 54(2), pages 323-58, March.
  10. McLennan, Andrew, 1989. "The Space of Conditional Systems is a Ball," International Journal of Game Theory, Springer, vol. 18(2), pages 125-39.
  11. Ritzberger, Klaus, 2002. "Foundations of Non-Cooperative Game Theory," OUP Catalogue, Oxford University Press, number 9780199247868, September.
  12. Hendon, Ebbe & Jacobsen, Hans Jorgen & Sloth, Birgitte, 1996. "The One-Shot-Deviation Principle for Sequential Rationality," Games and Economic Behavior, Elsevier, vol. 12(2), pages 274-282, February.
  13. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
  14. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Choice under Uncertainty," Econometrica, Econometric Society, vol. 59(1), pages 61-79, January.
  15. Carlos Pimienta & Cristian Litan, 2008. "Conditions for equivalence between sequentiality and subgame perfection," Economic Theory, Springer, vol. 35(3), pages 539-553, June.
  16. Fudenberg, Drew & Tirole, Jean, 1991. "Perfect Bayesian equilibrium and sequential equilibrium," Journal of Economic Theory, Elsevier, vol. 53(2), pages 236-260, April.
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