The challenge of non-zero-sum stochastic games

For a broad definition of time-discrete stochastic games, their zero-sum varieties have values. But the existence of ϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}-equilibrium for the corresponding non-zero-sum games has proven elusive. We present the problems associated with ϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}-equilibria in non-zero-sum stochastic games, from both the perspectives of proving existence and demonstrating a counter-example.