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    Rights statement: © 2014 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/).

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Stochastic fictitious play with continuous action sets

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>07/2014
<mark>Journal</mark>Journal of Economic Theory
Volume152
Number of pages35
Pages (from-to)179-213
Publication StatusPublished
<mark>Original language</mark>English

Abstract

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.

Bibliographic note

© 2014 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/).