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From posteriors to priors via cycles

Listed author(s):
  • Rodrigues-Neto, José Alvaro

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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Barton L. Lipman, 2003. "Finite Order Implications of Common Priors," Econometrica, Econometric Society, vol. 71(4), pages 1255-1267, 07.
  2. Samet, Dov, 1998. "Common Priors and Separation of Convex Sets," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 172-174, July.
  3. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
  4. John Geanakoplos, 1992. "Common Knowledge," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 53-82, Fall.
  5. Ng, Man-Chung, 2003. "On the duality between prior beliefs and trading demands," Journal of Economic Theory, Elsevier, vol. 109(1), pages 39-51, March.
  6. 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.
  7. Samet, Dov, 1998. "Iterated Expectations and Common Priors," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 131-141, July.
  8. 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.
  9. Larry Samuelson, 2004. "Modeling Knowledge in Economic Analysis," Journal of Economic Literature, American Economic Association, vol. 42(2), pages 367-403, June.
  10. John Geanakoplos & Heracles M. Polemarchakis, 1982. "We Can't Disagree Forever," Cowles Foundation Discussion Papers 639, Cowles Foundation for Research in Economics, Yale University.
  11. Morris, Stephen, 1994. "Trade with Heterogeneous Prior Beliefs and Asymmetric Information," Econometrica, Econometric Society, vol. 62(6), pages 1327-1347, November.
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