How common are common priors?

Ziv Hellman () and Dov Samet

Games and Economic Behavior, 2012, vol. 74, issue 2, 517-525

Abstract: To answer the question in the title we vary agentsʼ 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 agentʼs knowledge results in an increase in common knowledge. We show that for partition profiles that are tight the set of consistent type profiles is topologically large, while for partition profiles that are not tight this set is topologically small.

Keywords: Common prior; Common knowledge; Knowledge; Belief (search for similar items in EconPapers)
JEL-codes: D82 D83 (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (13)

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Working Paper: How Common Are Common Priors? (2010)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:74:y:2012:i:2:p:517-525

DOI: 10.1016/j.geb.2011.08.008

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