Home > Research > Publications & Outputs > Stochastic fictitious play with continuous acti...

Electronic data

  • 1-s2.0-S0022053114000623-main

    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/).

    Final published version, 647 KB, PDF document

    Available under license: CC BY

Links

Text available via DOI:

View graph of relations

Stochastic fictitious play with continuous action sets

Research output: Contribution to journalJournal articlepeer-review

Published

Standard

Stochastic fictitious play with continuous action sets. / Perkins, S.; Leslie, D. S.

In: Journal of Economic Theory, Vol. 152, 07.2014, p. 179-213.

Research output: Contribution to journalJournal articlepeer-review

Harvard

Perkins, S & Leslie, DS 2014, 'Stochastic fictitious play with continuous action sets', Journal of Economic Theory, vol. 152, pp. 179-213. https://doi.org/10.1016/j.jet.2014.04.008

APA

Vancouver

Author

Perkins, S. ; Leslie, D. S. / Stochastic fictitious play with continuous action sets. In: Journal of Economic Theory. 2014 ; Vol. 152. pp. 179-213.

Bibtex

@article{d2b05cea947a4a019fe6b5278226aa61,
title = "Stochastic fictitious play with continuous action sets",
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.",
keywords = "Stochastic fictitious play, Learning in games , Continuous action set games , Abstract stochastic approximation",
author = "S. Perkins and Leslie, {D. S.}",
note = "{\textcopyright} 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/).",
year = "2014",
month = jul,
doi = "10.1016/j.jet.2014.04.008",
language = "English",
volume = "152",
pages = "179--213",
journal = "Journal of Economic Theory",
issn = "0022-0531",
publisher = "ELSEVIER ACADEMIC PRESS INC",

}

RIS

TY - JOUR

T1 - Stochastic fictitious play with continuous action sets

AU - Perkins, S.

AU - Leslie, D. S.

N1 - © 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/).

PY - 2014/7

Y1 - 2014/7

N2 - 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.

AB - 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.

KW - Stochastic fictitious play

KW - Learning in games

KW - Continuous action set games

KW - Abstract stochastic approximation

U2 - 10.1016/j.jet.2014.04.008

DO - 10.1016/j.jet.2014.04.008

M3 - Journal article

VL - 152

SP - 179

EP - 213

JO - Journal of Economic Theory

JF - Journal of Economic Theory

SN - 0022-0531

ER -