Zero-determinant strategy of finite games with implementation errors and its application into group decision-making

The zero-determinant (ZD) strategy provides a new perspective for describing the interaction between players, and the errors among them will be an important role in designing ZD strategy, which attracts a lot of researches in various fields. This paper investigates how to design ZD strategy for multiplayer two-strategy repeated finite game under implementation errors. First, the implementation errors can be introduced by breaking down the probabilities of different possible cases, and the model of strategy transition process can be constructed with the semi-tensor product (STP) of matrices. Second, through the classical ZD strategy acquisition method, the step for designing ZD strategy for multiplayer two-strategy repeated finite games under implementation errors is presented. Then, the sufficient and necessary conditions for checking the effectiveness of ZD strategy under implementation errors are studied. In addition, by distinguishing the focal player's neighbors, the current approach is extended to networked evolutionary game (NEG) under implementation errors for group decision-making, and an intelligent algorithm is also provided. Finally, we use two examples to demonstrate the validity of our proposed method.