A probabilistic-numerical approximation for an obstacle problem arising in game theory

TL;DR

This paper develops a probabilistic-numerical method to approximate the value function of a two-player zero-sum stochastic differential game with asymmetric information, modeled by a quasilinear PDE with obstacle.

Contribution

It introduces a novel numerical scheme for solving the obstacle PDE associated with the game, accounting for asymmetric information.

Findings

The scheme effectively approximates the value function in the game.

The approach handles the obstacle constraint in the PDE.

Numerical experiments demonstrate accuracy and robustness.

Abstract

We investigate a two-player zero-sum stochastic differential game in which one of the players has more information on the game than his opponent. We show how to construct numerical schemes for the value function of this game, which is given by the solution of a quasilinear partial differential equation with obstacle.