It is well known that the rock-paper-scissors game has no pure saddle point. Weshow that this holds more generally: A symmetric two-player zero-sum game hasa pure saddle point if and only if it is not a generalized rock-paper-scissors game.Moreover, we show that every finite symmetric...

We show that for many classes of symmetric two-player games, the simple decision rule \imitate-the-best" can hardly be beaten by any other decision rule. Weprovide necessary and sufficient conditions for imitation to be unbeatable and showthat it can only be beaten by much in games that are of...