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Fictitious play in 3 x 3 games : chaos and dithering behaviour
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Strien, Sebastian van 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. doi:10.1016/j.geb.2010.12.004 ISSN 0899-8256.
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Official URL: http://dx.doi.org/10.1016/j.geb.2010.12.004
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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Game theory | ||||
Journal or Publication Title: | Games and Economic Behavior | ||||
Publisher: | Elsevier | ||||
ISSN: | 0899-8256 | ||||
Official Date: | September 2011 | ||||
Dates: |
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Volume: | Vol.73 | ||||
Number: | No.1 | ||||
Page Range: | pp. 262-286 | ||||
DOI: | 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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