joint work with Panayotis Mertikopoulos
We examine the convergence of a broad class of distributed learning dynamics for games with continuous action sets. The dynamics comprise a multi-agent generalization of Nesterov’s dual averaging method, a primal-dual mirror descent method that has seen a major resurgence in large-scale optimization and machine learning. To account for settings with high temporal variability we adopt a continuous-time formulation of dual averaging and we investigate the dynamics’ behavior when players have noiseless or noisy information. Asymptotic and non-asymptotic converegence results are presented.
In this talk I will briefly discuss the Best Reply Strategy (BRS) – an instantaneous response to a cost function – and how it can be related to a Mean Field Game (MFG) through a short-time rescaling. I will then focus on stationary solutions to linear-quadratic MFGs and the BRS, describing a proof for existence and uniqueness of such MFGs and comparing existence between the two models. I will highlight some specific examples of MFGs and BRS that show typical differences between the two models. Finally, I will explain the importance of these differences and their modelling consequences.
joint work with Sonja Steffensen, Michael Herty
We discuss an application motivated two level game with a large amount of players. To overcome the challenge of high dimensionality due to the number of players, we derive the mean field limit of infinitely many players. We discuss the relation between optimization and mean field limit for different settings and establish conditions for consistency.