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Topics arising from fictitious play dynamics
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Ostrovski, Georg (2013) Topics arising from fictitious play dynamics. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b2697305~S1
Abstract
In this thesis, we present a few different topics arising in the study of the learning dynamics
called fictitious play. We investigate the combinatorial properties of this dynamical system
describing the strategy sequences of the players, and in particular deduce a combinatorial
classification of zero-sum games with three strategies per player. We further obtain results
about the limit sets and asymptotic payoff performance of fictitious play as a learning
algorithm.
In order to study coexistence of regular (periodic and quasi-periodic) and chaotic
behaviour in fictitious play and a related continuous, piecewise affne flow on the threesphere,
we look at its planar first return maps and investigate several model problems for
such maps. We prove a non-recurrence result for non-self maps of regions in the plane,
similar to Brouwer’s classical result for planar homeomorphisms. Finally, we consider a
family of piecewise affne maps of the square, which is very similar to the first return maps
of fictitious play, but simple enough for explicit calculations, and prove several results about
its dynamics, particularly its invariant circles and regions.
Item Type: | Thesis (PhD) |
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Subjects: | Q Science > QA Mathematics |
Library of Congress Subject Headings (LCSH): | Game theory, Dynamics |
Official Date: | October 2013 |
Institution: | University of Warwick |
Theses Department: | Mathematics Institute |
Thesis Type: | PhD |
Publication Status: | Unpublished |
Supervisor(s)/Advisor: | Strien, Sebastian van, 1956- |
Sponsors: | Engineering and Physical Sciences Research Council (EPSRC); Warwick Postgraduate Research Fellowship |
Extent: | v, 125 leaves : charts |
Language: | eng |
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