A game theoretical approach for a nonlinear system driven by elliptic operators

This talk is based on the interplay between partial differential equations and probability. We find approximations using game theory to viscosity solutions to an elliptic system governed by two different operators(the Laplacian and the infinity Laplacian). We analyze a game that combines Tug - of -War with Random Walks in two different boards with a positive probability of jumping from one board to the other and we prove that the value functions for this game converge uniformly to a viscosity solution of an elliptic system as the step size goes to zero. In addition, we show uniqueness for the elliptic system using pure PDE techniques. Joint work with A.Miranda(Buenos Aires).