ABSTRACT
The game described in Appendix E was played under the assumption that it was to be played only once. Hence, once R and C have selected their strategies, the result of the game is determined. Suppose, however, that a sequence of games is to be played and that R and C are permitted to change their strategies from game to game. How should they proceed then? Since each contestant assumes that the other is just as intelligent as he is, they dare not develop a systematic pattern of choosing strategies for fear of this being discovered; hence, it would be advisable for them to choose their successive strategies by means of some random scheme. This can be accomplished by having R select a sect of probabilities p1, p2, …, pm that will determine the relative frequencies with which he wishes his strategies R1, R2, …, Rm to be played. Similarly, C is permitted to select a set of probabilities q1, q2, …, qn that will determine the relative frequencies with which he wishes his strategies C1, C2, …, Cn to be played.
