Sparrow, Colin, Strien, Sebastian van, 1956- and Harris, Christopher, 1960-. (2008) Fictitious play in 3 x 3 games : the transition between periodic and chaotic behaviour. Games and Economic Behavior, Vol.63 (No.1). pp. 259-291. ISSN 0899-8256

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Abstract

In the 1960s Shapley provided an example of a two-player fictitious game with periodic behaviour. In this game, player A aims to copy B's behaviour and player B aims to play one ahead of player A. In this paper we generalise Shapley's example by introducing an external parameter. We show that the periodic behaviour in Shapley's example at some critical parameter value disintegrates into unpredictable (chaotic) behaviour, with players dithering a huge number of times between different strategies. At a further critical parameter the dynamics becomes periodic again, but now both players aim to play one ahead of the other. In this paper we adopt a geometric (dynamical systems) approach. Here we prove rigorous results on continuity of the dynamics and on the periodic behaviour, while in the sequel to this paper we shall describe the chaotic behaviour. Crown Copyright (c) 2007 Published by Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Game theory, Chaotic behavior in systems, Bifurcation theory
Journal or Publication Title:	Games and Economic Behavior
Publisher:	Elsevier
ISSN:	0899-8256
Date:	May 2008
Volume:	Vol.63
Number:	No.1
Number of Pages:	33
Page Range:	pp. 259-291
Identification Number:	10.1016/j.geb.2007.08.005
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/29949

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