  In this tutorial, we provide an introduction to machine learning methods for
finding Nash equilibria in games with large number of agents. These types of
problems are important for the operations research community because of their
applicability to real life situations such as control of epidemics, optimal
decisions in financial markets, electricity grid management, or traffic control
for self-driving cars. We start the tutorial by introducing stochastic optimal
control problems for a single agent, in discrete time and in continuous time.
Then, we present the framework of dynamic games with finite number of agents.
To tackle games with a very large number of agents, we discuss the paradigm of
mean field games, which provides an efficient way to compute approximate Nash
equilibria. Based on this approach, we discuss machine learning algorithms for
such problems. First in the context of discrete time games, we introduce fixed
point based methods and related methods based on reinforcement learning.
Second, we discuss machine learning methods that are specific to continuous
time problems, by building on optimality conditions phrased in terms of
stochastic or partial differential equations. Several examples and numerical
illustrations of problems arising in operations research are provided along the
way.
