Abstract
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 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.
| Original language | English |
|---|---|
| Pages (from-to) | 517-525 |
| Number of pages | 9 |
| Journal | Games and Economic Behavior |
| Volume | 74 |
| Issue number | 2 |
| DOIs | |
| State | Published - Mar 2012 |
| Externally published | Yes |
Bibliographical note
Funding Information:✩ The research of the first author has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007–2013)/ERC grant agreement No. 249159. The research of the second author was partially financed by the Henry Crown Institute of Business Research in Israel. * Corresponding author. E-mail addresses: [email protected] (Z. Hellman), [email protected] (D. Samet).
Funding
✩ The research of the first author has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007–2013)/ERC grant agreement No. 249159. The research of the second author was partially financed by the Henry Crown Institute of Business Research in Israel. * Corresponding author. E-mail addresses: [email protected] (Z. Hellman), [email protected] (D. Samet).
| Funders | Funder number |
|---|---|
| FP7/2007 | |
| Henry Crown Institute of Business Research in Israel | |
| European Commission | 249159 |
| Seventh Framework Programme |
Keywords
- Belief
- Common knowledge
- Common prior
- Knowledge