• Corpus ID: 11301131

# Evolutionary stability implies asymptotic stability under multiplicative weights

@article{Avramopoulos2016EvolutionarySI,
title={Evolutionary stability implies asymptotic stability under multiplicative weights},
author={Ioannis C. Avramopoulos},
journal={ArXiv},
year={2016},
volume={abs/1601.07267}
}
We show that evolutionarily stable states in general (nonlinear) population games (which can be viewed as continuous vector fields constrained on a polytope) are asymptotically stable under a multiplicative weights dynamic (under appropriate choices of a parameter called the learning rate or step size, which we demonstrate to be crucial to achieve convergence, as otherwise even chaotic behavior is possible to manifest). Our result implies that evolutionary theories based on multiplicative…
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