  We study the emergence of chaotic behavior of Follow-the-Regularized Leader
(FoReL) dynamics in games. We focus on the effects of increasing the population
size or the scale of costs in congestion games, and generalize recent results
on unstable, chaotic behaviors in the Multiplicative Weights Update dynamics to
a much larger class of FoReL dynamics. We establish that, even in simple linear
non-atomic congestion games with two parallel links and any fixed learning
rate, unless the game is fully symmetric, increasing the population size or the
scale of costs causes learning dynamics to become unstable and eventually
chaotic, in the sense of Li-Yorke and positive topological entropy.
Furthermore, we show the existence of novel non-standard phenomena such as the
coexistence of stable Nash equilibria and chaos in the same game. We also
observe the simultaneous creation of a chaotic attractor as another chaotic
attractor gets destroyed. Lastly, although FoReL dynamics can be strange and
non-equilibrating, we prove that the time average still converges to an exact
equilibrium for any choice of learning rate and any scale of costs.
