Family of chaotic maps from game theory

From a two-agent, two-strategy congestion game where both agents apply the multiplicative weights update algorithm, we obtain a two-parameter family of maps of the unit square to itself. Interesting dynamics arise on the invariant diagonal, on which a two-parameter family of bimodal interval maps ex...

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Bibliographic Details
Published inDynamical systems (London, England) Vol. 36; no. 1; pp. 48 - 63
Main Authors Chotibut, Thiparat, Falniowski, Fryderyk, Misiurewicz, Michał, Piliouras, Georgios
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.01.2021
Taylor & Francis Ltd
Subjects
Algorithms
centre of mass
Chaos
Chaos theory
congestion game
Game theory
interval maps
multiplicative weights
Orbits
Parameters
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Summary:From a two-agent, two-strategy congestion game where both agents apply the multiplicative weights update algorithm, we obtain a two-parameter family of maps of the unit square to itself. Interesting dynamics arise on the invariant diagonal, on which a two-parameter family of bimodal interval maps exhibits periodic orbits and chaos. While the fixed point b corresponding to a Nash equilibrium of such map f is usually repelling, it is globally Cesàro attracting on the diagonal, that is, for every . This solves a known open question whether there exists a 'natural' nontrivial smooth map other than with centres of mass of all periodic orbits coinciding. We also study the dependence of the dynamics on the two parameters.
ISSN:1468-9367
1468-9375
DOI:10.1080/14689367.2020.1795624