Design of zero-determinant strategies and its application to networked repeated games

Using the semi-tensor product (STP) of matrices, the profile evolutionary equation (PEE) for repeated finite games is obtained. By PEE, the zero-determinant (ZD) strategies are developed for general finite games. A formula is then obtained to design ZD strategies for general finite games with multiple players and asymmetric strategies. A necessary and sufficient condition is obtained to ensure the availability of the designed ZD strategies. It follows that player i can unilaterally design k_i − 1 (one less than the number of its strategies) dominating linear relations about the expected payoffs of all players. Finally, the fictitious opponent player is proposed for networked repeated games (NRGs). A technique is proposed to simplify the model by reducing the number of frontier strategies.