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From posteriors to priors via cycles

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Author Info

  • Rodrigues-Neto, José Alvaro

Abstract

We present new necessary and sufficient conditions for checking if a set of players' posteriors may come from a common prior. A simple diagrammatic device calculates the join and meet of players' knowledge partitions. Each cycle in the diagram has a corresponding cycle equation. Posteriors are consistent with a common prior if and only if all cycle equations are satisfied. We prove that in games of two players, where the join partition has only singletons, a common prior exists if each player's distribution of beliefs over the elements of her opponent's partition is independent of her own private information.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 144 (2009)
Issue (Month): 2 (March)
Pages: 876-883

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Handle: RePEc:eee:jetheo:v:144:y:2009:i:2:p:876-883

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Web page: http://www.elsevier.com/locate/inca/622869

Related research

Keywords: Consistency Cycle Incomplete information Join Knowledge Meet Partition Prior Posterior Type;

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Cited by:
  1. Ziv Hellman, 2012. "Countable Spaces and Common Priors," Discussion Paper Series dp604, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  2. Jose Alvaro Rodrigues-Neto, 2011. "The Cycles Approach," ANU Working Papers in Economics and Econometrics 2011-547, Australian National University, College of Business and Economics, School of Economics.
  3. Martin Hellwig, 2011. "From Posteriors to Priors via Cycles: An Addendum," Working Paper Series of the Max Planck Institute for Research on Collective Goods 2011_07, Max Planck Institute for Research on Collective Goods.
  4. Ziv Hellman & Dov Samet, 2010. "How Common Are Common Priors?," Discussion Paper Series dp532, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  5. José Alvaro Rodrigues-Neto, 2012. "Cycles of length two in monotonic models," ANU Working Papers in Economics and Econometrics 2012-587, Australian National University, College of Business and Economics, School of Economics.
  6. José Alvaro Rodrigues-Neto, 2012. "Monotonic models and cycles," ANU Working Papers in Economics and Econometrics 2012-586, Australian National University, College of Business and Economics, School of Economics.
  7. 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.

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