  We consider the problem of representing collective behavior of large
populations and predicting the evolution of a population distribution over a
discrete state space. A discrete time mean field game (MFG) is motivated as an
interpretable model founded on game theory for understanding the aggregate
effect of individual actions and predicting the temporal evolution of
population distributions. We achieve a synthesis of MFG and Markov decision
processes (MDP) by showing that a special MFG is reducible to an MDP. This
enables us to broaden the scope of mean field game theory and infer MFG models
of large real-world systems via deep inverse reinforcement learning. Our method
learns both the reward function and forward dynamics of an MFG from real data,
and we report the first empirical test of a mean field game model of a
real-world social media population.
