When considering N-player differential games, making the approximation that there are instead infinitely many agents leads to the mean-field games system of PDEs. This system has two unknowns, the probability distribution of the players, and the value function being optimized by a representative agent. One of these satisfies a forward parabolic equation and the other satisfies a backward parabolic equation. The forward parabolic equation comes with initial data while terminal data (at a fixed time T > 0) is specified for the backward parabolic equation. We will describe some existence results for this coupled forward-backward system, without assuming that the non-linearity (the Hamiltonian) has any special structures such as convexity or monotonicity. Results presented will including treating a specific system which has been given as a model of household savings and wealth.
This video was produced by the SITE Research Center at New York University, as part of their talk series.
