van Strien, Sebastian and Sparrow, Colin. (2011) Fictitious play in 3 x 3 games : chaos and dithering behaviour. Games and Economic Behavior, Vol.73 (No.1). pp. 262-286. ISSN 0899-8256

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Abstract

In the 60's 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 continue to study a family of games which generalize Shapley's example by introducing an external parameter, and prove that there exists an abundance of periodic and chaotic behavior with players dithering between different strategies. The reason for all this, is that there exists a periodic orbit (consisting of playing mixed strategies) which is of 'jitter type': such an orbit is neither attracting, repelling or of saddle type as nearby orbits jitter closer and further away from it in a manner which is reminiscent of a random walk motion. We prove that this behaviour holds for an open set of games.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Game theory
Journal or Publication Title:	Games and Economic Behavior
Publisher:	Elsevier
ISSN:	0899-8256
Date:	September 2011
Volume:	Vol.73
Number:	No.1
Page Range:	pp. 262-286
Identification Number:	10.1016/j.geb.2010.12.004
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/38657

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