In this paper, we are concerned with game-theoretic interpretations to the following oblique derivative boundary value problem \(\begin{aligned} \left\{ \begin{array}{ll} \Delta _{p}^{N}u=0 & \text {in} \,\,\, \Omega ,\\ \langle \beta , Du \rangle + \gamma u = \gamma G & \text {on} \,\,\, \partial \Omega ,\\ \end{array} \right. \end{aligned}\) where \(\Delta _{p}^{N}\) is the normalized p-Laplacian. This problem can be regarded as a generalized version of the Robin boundary value problem for the Laplace equations. We construct several types of stochastic games associated with this problem by using ‘shrinking tug-of-war’. For the value functions of such games, we investigate the properties such as existence, uniqueness, regularity and convergence.
