Countable spaces and common priors

Ziv Hellman

doi:10.1007/s00182-013-0390-x

Countable spaces and common priors

Ziv Hellman

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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 language	English
Pages (from-to)	193-213
Number of pages	21
Journal	International Journal of Game Theory
Volume	43
Issue number	1
DOIs	https://doi.org/10.1007/s00182-013-0390-x
State	Published - Feb 2014
Externally published	Yes

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.

Funding

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.

Funders	Funder number
Seventh Framework Programme	249159
European Commission
Israel Science Foundation	212/09, 538/11
Seventh Framework Programme

Keywords

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

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10.1007/s00182-013-0390-x

Cite this

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Countable spaces and common priors

Abstract

Bibliographical note

Funding

Keywords

Access to Document

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