Approximate solutions of continuous-time stochastic games

TL;DR

This paper introduces a method to approximate the value function of zero-sum continuous-time stochastic differential games by using a model game with different dynamics, leading to a system of ODEs.

Contribution

It presents a novel approach to estimate the value function of complex stochastic games through a simplified model and differential equations.

Findings

Approximate value functions can be obtained via countable systems of ODEs.

The method provides bounds and estimates for the original game.

Applicable to a class of zero-sum stochastic differential games.

Abstract

The paper is concerned with a zero-sum continuous-time stochastic differential game with a dynamics controlled by a Markov process and a terminal payoff. The value function of the original game is estimated using the value function of a model game. The dynamics of the model game differs from the original one. The general result applied to differential games yields the approximation of value function of differential game by the solution of countable system of ODEs.