Percolation games
Guillaume Garnier, Bruno Ziliotto

TL;DR
This paper introduces a stochastic game model on integer lattices that serves as a simplified framework for studying the stochastic homogenization of Hamilton-Jacobi equations, providing convergence conditions and theoretical insights.
Contribution
It presents a new class of discrete-time stochastic games on $ abla^d$, linking game theory with homogenization of PDEs and establishing convergence criteria.
Findings
Conditions for the convergence of the n-stage game value.
Connections established between the game model and homogenization theory.
Discussion of implications for stochastic homogenization of Hamilton-Jacobi equations.
Abstract
This paper introduces a discrete-time stochastic game class on , 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 -stage game value converges as tends to infinity, and connections with homogenization theory is discussed.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Mathematical Modeling in Engineering · Stochastic processes and statistical mechanics
