In this presentation, I will show that there is a formal, but deep, link between an important class of Mean Field Games models (the "quadratic Mean Field Games) and the nonlinear Schrödinger (or Gross-Pitaevskii) equation encountered in many circumstances in physics, and which describes in particular the evolution of a set of interacting bosons.
This link makes it possible to develop highly effective approximation schemes to solve the mean field game equations. I will discuss in particular how to obtain in this way an understanding both detailed and intuitive of a population dynamics model wherein the agents are under a strong incentive to coordinate themselves.
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