Bayesian Games With a Continuum of States
AbstractNegative results on the the existence of Bayesian equilibria when state spaces have the cardinality of the continuum have been attained in recent years. This has led to the natural question: are there conditions that characterise when Bayesian games over continuum state spaces have measurable Bayesian equilibria? We answer this in the affirmative. Assuming that each type has finite or countable support, measurable Bayesian equilibria may fail to exist if and only if the underlying common knowledge $\sigma$-algebra is non-separable. Furthermore, anomalous examples with continuum state spaces have been presented in the literature in which common priors exist over entire state spaces but not over common knowledge components. There are also spaces over which players can have no disagreement, but when restricting attention to common knowledge components disagreements can exist. We show that when the common knowledge $\sigma$-algebra is separable all these anomalies disappear.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp641.
Length: 26 pages
Date of creation: May 2013
Date of revision:
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-06-16 (All new papers)
- NEP-CTA-2013-06-16 (Contract Theory & Applications)
- NEP-GTH-2013-06-16 (Game Theory)
- NEP-MIC-2013-06-16 (Microeconomics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ilan Nehama).
If references are entirely missing, you can add them using this form.