Evolution of mixed strategies in monotone games

We consider the basic problem of approximating Nash equilibria in noncooperative games. For monotone games, we design continuous time flows which converge in an averaged sense to Nash equilibria. We also study mean field equilibria, which arise in the large player limit of symmetric noncooperative games. In this setting, we will additionally show that the approximation of mean field equilibria is possible under a suitable monotonicity hypothesis.