How Common Are Common Priors?
AbstractTo 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.
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Bibliographic InfoPaper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp532.
Length: 18 pages
Date of creation: Feb 2010
Date of revision:
Publication status: Forthcoming in Games and Economic Behavior
Other versions of this item:
- D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
- D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
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