Measurable selection for purely atomic games

Hellman, Z. and Levy, Y. J. (2019) Measurable selection for purely atomic games. Econometrica, 87(2), pp. 593-629. (doi: 10.3982/ecta15479)

Abstract

A general selection theorem is presented constructing a measurable mapping from a state space to a parameter space under the assumption that the state space can be decomposed as a collection of countable equivalence classes under a smooth equivalence relation. It is then shown how this selection theorem can be used as a general purpose tool for proving the existence of measurable equilibria in broad classes of several branches of games when an appropriate smoothness condition holds, including Bayesian games with atomic knowledge spaces, stochastic games with countable orbits, and graphical games of countable degree—examples of a subclass of games with uncountable state spaces that we term purely atomic games. Applications to repeated games with symmetric incomplete information and acceptable bets are also presented.

• Item Type: Articles
• Additional Information: The copyright to this article is held by the Econometric Society, http://www.econometricsociety.org/. It may be downloaded, printed and reproduced only for personal or classroom use. Absolutely no downloading or copying may be done for, or on behalf of, any for-profit commercial firm or for other commercial purpose without the explicit permission of the Econometric Society.
• 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: Econometrica
• Publisher: Econometric Society
• ISSN: 0012-9682
• ISSN (Online): 1468-0262
• Published Online: 25 March 2019
• Copyright Holders: Copyright © 2019 The Econometric Society
• First Published: First published in Econometrica 87(2): 593-629
• Publisher Policy: Reproduced in accordance with the publisher copyright policy