From posteriors to priors via cycles |
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Authors: | José Alvaro Rodrigues-Neto |
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Institution: | Australian National University, School of Economics, College of Business and Economics, H.W. Arndt Building 25A, Canberra, ACT 0200, Australia |
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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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Keywords: | D82 D83 |
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