A tutorial on Zero-sum Stochastic Games

Understand

Zero-sum stochastic games generalize the notion of Markov Decision Processes (i.e.

• controlled Markov chains, or stochastic dynamic programming) to the 2-player competitive case : two players jointly control the evolution of a state variable, and have opposite interests.
• These notes constitute a short mathematical introduction to the theory of such games.
• Section 1 presents the basic model with finitely many states and actions.