Nash equilibria for non zero-sum ergodic stochastic differential games

TL;DR

This paper investigates non zero-sum ergodic stochastic differential games, establishing their link with ergodic BSDEs and proving the existence of Nash equilibria under generalized conditions, including interactions among different player types.

Contribution

It introduces a novel connection between ergodic BSDEs and non zero-sum stochastic games, proving Nash equilibrium existence under broad conditions.

Findings

Existence of Nash equilibria under generalized Isaac's conditions

Connection established between ergodic BSDEs and stochastic games

Analysis of games with interacting players of different types

Abstract

In this paper we consider non zero-sum games where multiple players control the drift of a process, and their payoffs depend on its ergodic behaviour. We establish their connection with systems of Ergodic BSDEs, and prove the existence of a Nash equilibrium under the generalised Isaac's conditions. We also study the case of interacting players of different type.