Discounted stochastic games with no stationary Nash equilibrium: two examples

Levy, Y. (2013) Discounted stochastic games with no stationary Nash equilibrium: two examples. Econometrica, 81(5), pp. 1973-2007. (doi: 10.3982/ECTA10530)

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Abstract

We present two examples of discounted stochastic games, each with a continuum of states, finitely many players, and actions, that possess no stationary equilibria. The first example has deterministic transitions—an assumption undertaken in most of the early applications of dynamics games in economics—and perfect information, and does not possess even stationary approximate equilibria or Markovian equilibria. The second example satisfies, in addition to stronger regularity assumptions, that all transitions are absolutely continuous with respect to a fixed measure—an assumption that has been widely used in more recent economic applications. This assumption has been undertaken in several positive results on the existence of stationary equilibria in special cases, and in particular, guarantees the existence of stationary approximate equilibria.

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: Levy, Y.
College/School:College of Social Sciences > Adam Smith Business School > Economics
Journal Name:Econometrica
Publisher:Wiley
ISSN:0012-9682
ISSN (Online):1468-0262
Published Online:18 September 2013
Copyright Holders:Copyright © 2013 The Econometric Society
First Published:First published in Econometrica 81(5):1973-2007
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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