Percolation games

Percolation Games

Guillaume Garnier (1) , Bruno Ziliotto (2, 3, 4)

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 CNRS - Centre National de la Recherche Scientifique
4 PSL - Université Paris Sciences et Lettres

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 is discussed.

Domaines: Optimisation et contrôle [math.OC]

Guillaume Garnier, Bruno Ziliotto. Percolation games. Mathematics of Operations Research, In press, ⟨10.1287/moor.2022.1334⟩. ⟨hal-03406065⟩