Bayesian games with a continuum of states

Hellman, Z. and Levy, Y. J. (2017) Bayesian games with a continuum of states. Theoretical Economics, 12(3), pp. 1089-1120. (doi: 10.3982/TE1544)

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Abstract

We show that every Bayesian game with purely atomic types has a measurable Bayesian equilibrium when the common knowl- edge relation is smooth. Conversely, for any common knowledge rela- tion that is not smooth, there exists a type space that yields this common knowledge relation and payoffs such that the resulting Bayesian game will 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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Levy, Dr John
Authors: Hellman, Z., and Levy, Y. J.
College/School:College of Social Sciences > Adam Smith Business School > Economics
Journal Name:Theoretical Economics
Publisher:Econometric Society
ISSN:1933-6837
ISSN (Online):1555-7561
Published Online:22 September 2017
Copyright Holders:Copyright © 2017 The Authors
First Published:First published in Theoretical Economics 12(3): 1089-1120
Publisher Policy:Reproduced under a Creative Commons License
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