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How common are common priors?

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  • Hellman, Ziv
  • Samet, Dov

Abstract

To answer the question in the title we vary agentsʼ beliefs against the background of a fixed knowledge space, that is, a state space with a partition for each agent. Beliefs are the posterior probabilities of agents, which we call type profiles. We then ask what is the topological size of the set of consistent type profiles, those that are derived from a common prior (or a common improper prior in the case of an infinite state space). The answer depends on what we term the tightness of the partition profile. A partition profile is tight if in some state it is common knowledge that any increase of any single agentʼs knowledge results in an increase in common knowledge. We show that for partition profiles that are tight the set of consistent type profiles is topologically large, while for partition profiles that are not tight this set is topologically small.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 74 (2012)
Issue (Month): 2 ()
Pages: 517-525

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Handle: RePEc:eee:gamebe:v:74:y:2012:i:2:p:517-525

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Web page: http://www.elsevier.com/locate/inca/622836

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Keywords: Common prior; Common knowledge; Knowledge; Belief;

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References

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  1. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
  2. Faruk Gul, 1998. "A Comment on Aumann's Bayesian View," Econometrica, Econometric Society, vol. 66(4), pages 923-928, July.
  3. Robert J. Aumann, 1998. "Common Priors: A Reply to Gul," Econometrica, Econometric Society, vol. 66(4), pages 929-938, July.
  4. Robert J. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Working Paper Archive 661465000000000377, David K. Levine.
  5. Yaw Nyarko, 2010. "Most games violate the common priors doctrine," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(1), pages 189-194.
  6. Samet, Dov, 1998. "Iterated Expectations and Common Priors," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 131-141, July.
  7. Nyarko, Yaw, 1991. "Most Games Violate the Harsanyi Doctrine," Working Papers 91-39, C.V. Starr Center for Applied Economics, New York University.
  8. Rodrigues-Neto, José Alvaro, 2009. "From posteriors to priors via cycles," Journal of Economic Theory, Elsevier, vol. 144(2), pages 876-883, March.
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Citations

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Cited by:
  1. Rodrigues-Neto, José Alvaro, 2012. "The cycles approach," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 207-211.
  2. Martin Hellwig, 2011. "Incomplete-Information Models of Large Economies with Anonymity: Existence and Uniqueness of Common Priors," Working Paper Series of the Max Planck Institute for Research on Collective Goods 2011_08, Max Planck Institute for Research on Collective Goods.
  3. Ziv Hellman, 2012. "Countable Spaces and Common Priors," Discussion Paper Series dp604, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  4. Ziv Hellman, 2013. "Almost common priors," International Journal of Game Theory, Springer, vol. 42(2), pages 399-410, May.
  5. Collevecchio, Andrea & LiCalzi, Marco, 2012. "The probability of nontrivial common knowledge," Games and Economic Behavior, Elsevier, vol. 76(2), pages 556-570.
  6. Hellman, Ziv, 2013. "Weakly rational expectations," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 496-500.
  7. Hellwig, Martin F., 2013. "From posteriors to priors via cycles: An addendum," Economics Letters, Elsevier, vol. 118(3), pages 455-458.

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