In this talk, we are concerned with stochastic games related to PDEs.

We mainly discuss a sort of stochastic game called 'tug-of-war', which is a discretized scheme for the normalized p-Laplace operator $Delta_{p}^{N}$ defined by $Delta_{p}^{N}=Delta + (p-2)Delta_{infty}^{N}$. This approach is motivated by mean value characterizations for $p$-harmonic functions.

We present some mathematical results for the value functions of such games and investigate the relation between tug-of-war games and their model equations.

Furthermore, we will introduce problems related to this topic.