Iterated Expectations, Compact Spaces and Common Priors
Extending to infinite state spaces that are compact metric spaces a result previously attained by Dov Samet solely in the context of finite state spaces, a necessary and sufficient condition for the existence of a common prior for several players is given in terms of the players’ present beliefs only. A common prior exists if and only if for each random variable it is common knowledge that all its iterated expectations with respect to any permutation converge to the same value; this value is its expectation with respect to the common prior. It is further shown that the restriction to compact metric spaces is ‘natural’ when semantic type spaces are derived from syntactic models, and that compactness is a necessary condition. Many proofs are based on results from the theory of Markov chains.
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- Samet, Dov, 1998.
"Common Priors and Separation of Convex Sets,"
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- Giacomo Bonanno & Klaus Nehring, 1999. "How to make sense of the common prior assumption under incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 409-434.
- 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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- Nehring, Klaus, 2004. "The veil of public ignorance," Journal of Economic Theory, Elsevier, vol. 119(2), pages 247-270, December. Full references (including those not matched with items on IDEAS)