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We consider the problem of representing collective behavior of largepopulations and predicting the evolution of a population distribution over adiscrete state space. A discrete time mean field game (MFG) is motivated as aninterpretable model founded on game theory for understanding the aggregateeffect of individual actions and predicting the temporal evolution ofpopulation distributions. We achieve a synthesis of MFG and Markov decisionprocesses (MDP) by showing that a special MFG is reducible to an MDP. Thisenables us to broaden the scope of mean field game theory and infer MFG modelsof large real-world systems via deep inverse reinforcement learning. Our methodlearns 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 areal-world social media population.

Learning Deep Mean Field Games for Modeling Large Population Behavior