  Many real-world problems modeled by stochastic games have huge state and/or
action spaces, leading to the well-known curse of dimensionality. The
complexity of the analysis of large-scale systems is dramatically reduced by
exploiting mean field limit and dynamical system viewpoints. Under regularity
assumptions and specific time-scaling techniques, the evolution of the mean
field limit can be expressed in terms of deterministic or stochastic equation
or inclusion (difference or differential). In this paper, we overview recent
advances of large-scale games in large-scale systems. We focus in particular on
population games, stochastic population games and mean field stochastic games.
Considering long-term payoffs, we characterize the mean field systems using
Bellman and Kolmogorov forward equations.
