From posteriors to priors via cycles
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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- Barton L. Lipman, 2003.
"Finite Order Implications of Common Priors,"
Econometric Society, vol. 71(4), pages 1255-1267, 07.
- Samet, Dov, 1998.
"Common Priors and Separation of Convex Sets,"
Games and Economic Behavior,
Elsevier, vol. 24(1-2), pages 172-174, July.
- Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
- John Geanakoplos, 1992. "Common Knowledge," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 53-82, Fall.
- 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.
- Paul Milgrom & Nancy L.Stokey, 1979.
"Information, Trade, and Common Knowledge,"
377R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Samet, Dov, 1998. "Iterated Expectations and Common Priors," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 131-141, July.
- 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.
- Larry Samuelson, 2004. "Modeling Knowledge in Economic Analysis," Journal of Economic Literature, American Economic Association, vol. 42(2), pages 367-403, June.
- John Geanakoplos & Heracles M. Polemarchakis, 1982.
"We Can't Disagree Forever,"
Cowles Foundation Discussion Papers
639, Cowles Foundation for Research in Economics, Yale University.
- 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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