A Beginner's Tutorial on Strategy Complexity in Stochastic Games: Can the King Cautiously Eliminate Robin Hood?

This article is a tutorial introduction to stochastic games, first introduced by Shapley in 1953. The presentation is based around several classical examples of such games, and focusses on the question of strategy complexity in terms of parameters such as the cardinality of the state space, branching factor of the transition function, and whether the game is concurrent or turn-based. Our goal is to give a practical introduction to stochastic games, the notion of values and strategies, and the memory requirements of optimal and ε-optimal strategies in different games.