Existence of SPE in Discounted Stochastic Games; Revisited and Simplified

Mertens and Parthasarathy (1987) proved the existence of sub-game perfect equilibria in discounted stochastic games.  Their method involved new techniques in dynamic programming, which were presented in a very general framework, with no expense spared in highlighting versatility and scope.  This paper presents the fundamentals of their technique which are necessary, as well as identifies and elaborates on the components of their method, hence giving the core of the proof in a much more concise, direct, and illuminating manner.