Zero-sum stochastic games

Abstract

In this chapter, we describe a major part of the theory of zero-sum discrete-time stochastic games. We review all basic streams of research in this area, in the context of the existence of value and uniform value, algorithms, vector payoffs, incomplete information, and imperfect state observation. Also some models related to continuous-time games, e.g., games with short-stage duration, semi- Markov games, are mentioned. Moreover, a number of applications of stochastic games are pointed out. The provided reference list reveals a tremendous progress made in the field of zero-sum stochastic games since the seminal work of Shapley (Proc Nat Acad Sci USA 39:1095-1100, 1953).