Stochastic fictitious play with continuous action sets

Perkins, S. and Leslie, D. S. (2014) Stochastic fictitious play with continuous action sets. Journal of Economic Theory, 152. pp. 179-213. ISSN 0022-0531

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Continuous action space games are ubiquitous in economics. However, whilst learning dynamics in normal form games with finite action sets are now well studied, it is not until recently that their continuous action space counterparts have been examined. We extend stochastic fictitious play to the continuous action space framework. In normal form games with finite action sets the limiting behaviour of a discrete time learning process is often studied using its continuous time counterpart via stochastic approximation. In this paper we study stochastic fictitious play in games with continuous action spaces using the same method. This requires the asymptotic pseudo-trajectory approach to stochastic approximation to be extended to Banach spaces. In particular the limiting behaviour of stochastic fictitious play is studied using the associated smooth best response dynamics on the space of finite signed measures. Using this approach, stochastic fictitious play is shown to converge to an equilibrium point in two-player zero-sum games and a stochastic fictitious play-like process is shown to converge to an equilibrium in negative definite single population games.

Item Type:
Journal Article
Journal or Publication Title:
Journal of Economic Theory
Additional Information:
© 2014 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (
Uncontrolled Keywords:
?? stochastic fictitious playlearning in games continuous action set games abstract stochastic approximationeconomics and econometrics ??
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Deposited On:
16 Sep 2014 10:38
Last Modified:
19 Dec 2023 01:23