Game Theoretical Methods in Nonlinear PDEs

Abstract

Nonlinear PDEs, mean value properties, and stochastic differential games are intrinsically connected. In this short expository note, we will describe how the solutions to certain PDEs (of $p$-Laplacian type) can be interpreted as limits of values of a specific Tug-of-War game, when the step-size $\epsilon$ determining the allowed length of move of a token, decreases to $0$.