Percolation Games

This paper introduces a discrete-time stochastic game class on ${\mathbb{Z}}^d$, which plays the role of a toy model for the well-known problem of stochastic homogenization of Hamilton–Jacobi equations. Conditions are provided under which the n-stage game value converges as n tends to infinity, and connections with homogenization theory are discussed.

Funding: The second author acknowledges the support of the French Agence Nationale de la Recherche (ANR) [Grant ANR-21-CE40-0020] (CONVERGENCE project).