6 research outputs found
Scaling up Mean Field Games with Online Mirror Descent
We address scaling up equilibrium computation in Mean Field Games (MFGs)
using Online Mirror Descent (OMD). We show that continuous-time OMD provably
converges to a Nash equilibrium under a natural and well-motivated set of
monotonicity assumptions. This theoretical result nicely extends to
multi-population games and to settings involving common noise. A thorough
experimental investigation on various single and multi-population MFGs shows
that OMD outperforms traditional algorithms such as Fictitious Play (FP). We
empirically show that OMD scales up and converges significantly faster than FP
by solving, for the first time to our knowledge, examples of MFGs with hundreds
of billions states. This study establishes the state-of-the-art for learning in
large-scale multi-agent and multi-population games
-player games and mean field games of moderate interactions
We study the asymptotic organization among many optimizing individuals
interacting in a suitable "moderate" way. We justify this limiting game by
proving that its solution provides approximate Nash equilibria for large but
finite player games. This proof depends upon the derivation of a law of large
numbers for the empirical processes in the limit as the number of players tends
to infinity. Because it is of independent interest, we prove this result in
full detail. We characterize the solutions of the limiting game via a
verification argument