Countable spaces and common priors

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We show that the no betting characterisation of the existence of common priors over finite type spaces extends only partially to improper priors in the countably infinite state space context: the existence of a common prior implies the absence of a bounded agreeable bet, and the absence of a common improper prior implies the existence of a bounded agreeable bet. However, a type space that lacks a common prior but has a common improper prior may or may not have a bounded agreeable bet. As a side-benefit of the proofs here, we also obtain a constructive proof of the no betting characterisation in finite spaces.

Original languageEnglish
Pages (from-to)193-213
Number of pages21
JournalInternational Journal of Game Theory
Issue number1
StatePublished - Feb 2014
Externally publishedYes

Bibliographical note

Funding Information:
The results in this paper formed part of the author’s PhD thesis, with the research supported in part by the European Research Council under the European Commission’s Seventh Framework Programme (FP7/2007–2013)/ERC Grant Agreement No. 249159, and by ISF Grants 538/11 and 212/09. Special thanks are due to Ehud Lehrer and Dov Samet for many helpful conversations as well as crucial assistance in formulating and proving Lemma 1 and Proposition 1. The author also thanks the anonymous referees for enabling a much improved presentation, and Aviad Heifetz for helpful correspondence.


  • Agreeing to disagree
  • Common priors
  • Improper priors
  • Knowledge and beliefs
  • No betting and no trade


Dive into the research topics of 'Countable spaces and common priors'. Together they form a unique fingerprint.

Cite this