Abstract
We show that every Bayesian game with purely atomic types has a measurable Bayesian equilibrium when the common knowledge relation is smooth. Conversely, for any common knowledge relation that is not smooth, there exists a type space that yields this common knowledge relation and payoffs such that the resulting Bayesian game does not have any Bayesian equilibrium. We show that our smoothness condition also rules out two paradoxes involving Bayesian games with a continuum of types: the impossibility of having a common prior on components when a common prior over the entire state space exists, and the possibility of interim betting/trade even when no such trade can be supported ex ante.
| Original language | English |
|---|---|
| Pages (from-to) | 1089-1120 |
| Number of pages | 32 |
| Journal | Theoretical Economics |
| Volume | 12 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 2017 |
Bibliographical note
Publisher Copyright:Copyright © 2017 The Authors.
Funding
Ziv Hellman: [email protected] Yehuda John Levy: [email protected] The research of the first author was supported in part by the European Research Council under the European Commission’s Seventh Framework Programme (FP7/2007–2013)/ERC Grant Agreement 249159, and in part by Israel Science Foundation Grants 538/11 and 212/09. The research of the second author was supported in part by Israel Science Foundation Grant 1596/10.
| Funders | Funder number |
|---|---|
| FP7/2007 | |
| Seventh Framework Programme | 249159 |
| European Commission | |
| Israel Science Foundation | 1596/10, 212/09, 538/11 |
| Seventh Framework Programme |
Keywords
- Bayesian equilibrium
- Bayesian games
- common priors
- continuum of states