Stationary Strategies in Zero-Sum Stochastic Games

We deal with zero-sum stochastic games. We demonstrate the importance of stationary strategies by showing that stationary strategies are better (in terms of the rewards they guarantee for a player, against any strategy of his opponent) than (1) pure strategies (even history-dependent ones), (2) strategies which may use only a finite number of different mixed actions in any state, and (3) strategies with finite recall. Examples are given to clarify the issues.