On approximate and weak correlated equilibria in constrained discounted stochastic games

TL;DR

This paper investigates the existence of approximate and weak correlated equilibria in constrained discounted stochastic games with continuous transition probabilities, extending to stationary Nash equilibria in specific stochastic game classes.

Contribution

It establishes the existence of approximate stationary and weak correlated equilibria in constrained discounted stochastic games with continuous transition probabilities.

Findings

Existence of approximate stationary equilibria.

Existence of stationary weak correlated equilibria.

Implication for stationary Nash equilibria in ARAT stochastic games.

Abstract

In this paper, we consider constrained discounted stochastic games with a countably generated state space and norm continuous transition probability having a density function. We prove existence of approximate stationary equilibria and stationary weak correlated equilibria. Our results imply the existence of stationary Nash equilibrium in $ARAT$ stochastic games.