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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Published in | Dynamical systems (London, England) Vol. 36; no. 1; pp. 48 - 63 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Abingdon
Taylor & Francis
02.01.2021
Taylor & Francis Ltd |
Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 1468-9367 1468-9375 |
DOI: | 10.1080/14689367.2020.1795624 |