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Finite Order Implications of Common Priors in Infinite Models

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  • Barton L. Lipman

    ()
    (Department of Economics, Boston University)

Abstract

Lipman [2003] shows that in a finite model, the common prior assumption has weak implications for finite orders of beliefs about beliefs. In particular, the only such implications are those stemming from the weaker assumption of a common support. To explore the role of the finite model assumption in generating this conclusion, this paper considers the finite order implications of common priors in a countable model. I show that in countable models, the common prior assumption also implies a tail consistency condition regarding beliefs. More specifically, I show that in a countable model, the finite order implications of the common prior assumption are the same as those stemming from the assumption that priors have a common support and have tail probabilities converging to zero at the same rate.

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Bibliographic Info

Paper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number WP2005-009.

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Length: 26 pages
Date of creation: Mar 2005
Date of revision:
Handle: RePEc:bos:wpaper:wp2005-009

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References

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  1. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February.
  2. Halpern, Joseph Y., 2002. "Characterizing the Common Prior Assumption," Journal of Economic Theory, Elsevier, vol. 106(2), pages 316-355, October.
  3. Barton L. Lipman, 1997. "Finite Order Implications of Common Priors," Game Theory and Information 9703005, EconWPA.
  4. HEIFETZ, Aviad, 2003. "The positive foundation of the common prior assumption," CORE Discussion Papers 2003052, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Samet, Dov, 1998. "Common Priors and Separation of Convex Sets," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 172-174, July.
  6. Giacomo Bonanno & Klaus Nehring, 1999. "How to make sense of the common prior assumption under incomplete information," International Journal of Game Theory, Springer, vol. 28(3), pages 409-434.
  7. Frankel, David M. & Morris, Stephen & Pauzner, Ady, 2003. "Equilibrium selection in global games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 108(1), pages 1-44, January.
  8. Heifetz, Aviad, 2006. "The positive foundation of the common prior assumption," Games and Economic Behavior, Elsevier, vol. 56(1), pages 105-120, July.
  9. Paul Milgrom & Nancy L.Stokey, 1979. "Information, Trade, and Common Knowledge," Discussion Papers 377R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. Jonathan Weinstein & Muhamet Yildiz, 2004. "Finite-Order Implications of Any Equilibrium," Levine's Working Paper Archive 122247000000000065, David K. Levine.
  11. Morris, Stephen, 1995. "The Common Prior Assumption in Economic Theory," Economics and Philosophy, Cambridge University Press, vol. 11(02), pages 227-253, October.
  12. Samet, Dov, 1998. "Iterated Expectations and Common Priors," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 131-141, July.
  13. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
  14. Jonathan Weinstein & Muhamet Yildiz, 2007. "A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements," Econometrica, Econometric Society, vol. 75(2), pages 365-400, 03.
  15. Robert J Aumann, 1999. "Agreeing to Disagree," Levine's Working Paper Archive 512, David K. Levine.
  16. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
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Cited by:
  1. Oyama, Daisuke & Tercieux, Olivier, 2005. "On the Strategic Impact of an Event under Non-Common Priors," MPRA Paper 4559, University Library of Munich, Germany.
  2. Daisuke Oyama & Olivier Tercieux, 2007. "Robust Equilibria under Non-Common Priors," Levine's Bibliography 843644000000000210, UCLA Department of Economics.

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