Tug-of-war games and PDEs

Abstract

We review some recent results concerning tug-of-war games and their relation to some well-known partial differential equations (PDEs). In particular, we will show that solutions to certain PDEs can be obtained as limits of values of tug-of-war games when the parameter that controls the length of the possible movements goes to zero. Since the equations being studied are nonlinear and are not in divergence form, we will make extensive use of the concept of viscosity solutions.