Abstract
The Multiplicative Weights Update (MWU) method is a ubiquitous meta-algorithm that works as follows: A distribution is maintained on a certain set, and at each step the probability assigned to action gamma is multiplied by (1 - epsilon C(gamma)) > 0 where C(gamma) is the "cost" of action gamma and then rescaled to ensure that the new values form a distribution. We analyze MWU in congestion games where agents use arbitrary admissible constants as learning rates epsilon and prove convergence to exact Nash equilibria. Interestingly, this convergence result does not carry over to the nearly homologous MWU variant where at each step the probability assigned to action gamma is multiplied by (1 - epsilon)(C(gamma)) even for the simplest case of two-agent, two-strategy load balancing games, where such dynamics can provably lead to limit cycles or even chaotic behavior.