Zero-determinant Strategy of Repeated Boolean Games with Time-delay

Zero-determinant (ZD) strategy for an iterated two-player Boolean game with time delay is investigated in this pa-per. Firstly, using semi-tensor product (STP) of matrices, evolutionary dynamic model of delayed two-player repeated Boolean games (TRBG) is obtained. Secondly, ZD strategy is proposed through which the player can enforce a linear augmented payoff relationship, so that he can literally determine his opponent's payoff. Finally, the effect of the length of a player's memory on ZD strategy has also been discussed. This paper reveals that players with longer memories do not have an advantage in TRBG, even if they are not independent of each other.