The Dynamic Programming approach to differential games
A zero-sum differential game is a dynamical system controlled by two players, coupled with a cost functional that one player wants to minimize and the other player seeks to maximize. If the value function of the game is defined appropriately, the classical dynamic programming approach leads to a Hamilton-Jacobi partial differential equation with nonconvex Hamiltonian, called Isaacs' equation. I will survey the results of various authors on the well-posedness of these equations in the framework of viscosity solutions, and on the use of PDE methods for the sinthesis of approximate optimal feedbacks for both players.
