How Common Are Common Priors?
To answer the question in the title we vary agents' beliefs against the background of a fixed knowledge space, that is, a state space with a partition for each agent. Beliefs are the posterior probabilities of agents, which we call type profiles. We then ask what is the topological size of the set of consistent type profiles, those that are derived from a common prior (or a common improper prior in the case of an infinite state space). The answer depends on what we term the tightness of the partition profile. A partition profile is tight if in some state it is common knowledge that any increase of any single agent's knowledge results in an increase in common knowledge. We show that for partition profiles which are tight the set of consistent type profiles is topologically large, while for partition profiles which are not tight this set is topologically small.
|Date of creation:||Feb 2010|
|Date of revision:|
|Publication status:||Forthcoming in Games and Economic Behavior|
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- Yaw Nyarko, 2010. "Most games violate the common priors doctrine," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(1), pages 189-194.
- Robert J. Aumann, 2010.
"Correlated Equilibrium as an expression of Bayesian Rationality,"
Levine's Working Paper Archive
661465000000000377, David K. Levine.
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- Nyarko, Yaw, 1991. "Most Games Violate the Harsanyi Doctrine," Working Papers 91-39, C.V. Starr Center for Applied Economics, New York University.
- Robert J. Aumann, 1998. "Common Priors: A Reply to Gul," Econometrica, Econometric Society, vol. 66(4), pages 929-938, 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.
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