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Finite order implications of common priors in infinite models

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  • Lipman, Barton L.

Abstract

Lipman [Lipman, B., 2003. Finite order implications of common priors, Econometrica, 71 (July), 1255-1267] 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 the simplest possible infinite model, namely, 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

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 46 (2010)
Issue (Month): 1 (January)
Pages: 56-70

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Handle: RePEc:eee:mateco:v:46:y:2010:i:1:p:56-70

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Web page: http://www.elsevier.com/locate/jmateco

Related research

Keywords: Common priors;

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References

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  1. Samet, Dov, 1998. "Iterated Expectations and Common Priors," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 131-141, July.
  2. Frankel, David M. & Morris, Stephen & Pauzner, Ady, 2003. "Equilibrium Selection in Global Games with Strategic Complementarities," Staff General Research Papers 11920, Iowa State University, Department of Economics.
  3. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
  4. Samet, Dov, 1998. "Common Priors and Separation of Convex Sets," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 172-174, July.
  5. 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.
  6. 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).
  7. Morris, Stephen, 1995. "The Common Prior Assumption in Economic Theory," Economics and Philosophy, Cambridge University Press, vol. 11(02), pages 227-253, October.
  8. Milgrom, Paul & Stokey, Nancy, 1982. "Information, trade and common knowledge," Journal of Economic Theory, Elsevier, vol. 26(1), pages 17-27, February.
  9. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
  10. Heifetz, Aviad, 2006. "The positive foundation of the common prior assumption," Games and Economic Behavior, Elsevier, vol. 56(1), pages 105-120, July.
  11. Barton L. Lipman, 2003. "Finite Order Implications of Common Priors," Econometrica, Econometric Society, vol. 71(4), pages 1255-1267, 07.
  12. Halpern, Joseph Y., 2002. "Characterizing the Common Prior Assumption," Journal of Economic Theory, Elsevier, vol. 106(2), pages 316-355, October.
  13. 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.
  14. Jonathan Weinstein & Muhamet Yildiz, 2004. "Finite-Order Implications of Any Equilibrium," Levine's Working Paper Archive 122247000000000065, David K. Levine.
  15. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February.
  16. Robert J Aumann, 1999. "Agreeing to Disagree," Levine's Working Paper Archive 512, David K. Levine.
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Cited by:
  1. Oyama, Daisuke & Tercieux, Olivier, 2005. "Robust Equilibria under Non-Common Priors," MPRA Paper 14287, University Library of Munich, Germany.
  2. Oyama, Daisuke & Tercieux, Olivier, 2012. "On the strategic impact of an event under non-common priors," Games and Economic Behavior, Elsevier, vol. 74(1), pages 321-331.

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