Section: New Results

Convergence of game dynamics

The study of game dynamics is crucial in understanding the long-run behavior of optimizing agents in an environment that changes dynamically over time, whether endogenously (i.e. via the agents' interactions) or exogenously (i.e. due to factors beyond the agents' influence). Starting with the observation that oblivious agents should seek to at least minimize their regret, we showed in [9] that players that "follow the regularized leader" in continuous time achieve no regret at an optimal rate. The multi-agent implications of this property where subsequently explored in [3], [24] (for games with finite and continuous action sets respectively), where we established a wide range of conditions guaranteeing convergence to Nash equilibrium, even when the players' payoff observations are subject to noise and/or other stochastic disturbances.