Approximate public-signal correlated equilibria for nonzero-sum differential games

TL;DR

This paper develops an approximate public-signal correlated equilibrium for nonzero-sum differential games using stochastic strategies with memory, connecting stochastic and deterministic game outcomes.

Contribution

It introduces a method to construct approximate equilibria in complex stochastic differential games and analyzes their limits as stochastic games approach deterministic ones.

Findings

Constructed approximate equilibria in stochastic differential games.

Showed the limit of equilibrium outcomes lies in the convex hull of deterministic strategies.

Bridged stochastic and deterministic game outcomes through equilibrium analysis.

Abstract

We construct an approximate public-signal correlated equilibrium for a nonzero-sum differential game in the class of stochastic strategies with memory. The construction is based on a solution of an auxiliary nonzero-sum continuous-time stochastic game. This class of games includes stochastic differential games and continuous-time Markov games. Moreover, we study the limit of approximate equilibrium outcomes in the case when the auxiliary stochastic games tend to the original deterministic one. We show that it lies in the convex hull of the set of equilibrium values provided by deterministic punishment strategies.