  We present two variants of a multi-agent reinforcement learning algorithm
based on evolutionary game theoretic considerations. The intentional simplicity
of one variant enables us to prove results on its relationship to a system of
ordinary differential equations of replicator-mutator dynamics type, allowing
us to present proofs on the algorithm's convergence conditions in various
settings via its ODE counterpart. The more complicated variant enables
comparisons to Q-learning based algorithms. We compare both variants
experimentally to WoLF-PHC and frequency-adjusted Q-learning on a range of
settings, illustrating cases of increasing dimensionality where our variants
preserve convergence in contrast to more complicated algorithms. The
availability of analytic results provides a degree of transferability of
results as compared to purely empirical case studies, illustrating the general
utility of a dynamical systems perspective on multi-agent reinforcement
learning when addressing questions of convergence and reliable generalisation.
