Automata for Repeated Games

The possibility of repetition usually forms part of the definition of a ‘game’. In game theory, it is often tacitly assumed that the game situation is repeated many times. A mixed strategy, for instance, is interpreted in the sense that a player chooses a certain move with a certain frequency. In fictitious games, it is taken for granted that the reply move is chosen as optimal answer to the average of the moves hitherto taken by the opponent.