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.

中文翻译：

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具有实现错误的有限博弈的零行定式策略及其在群体决策中的应用


零行列式 （ZD） 策略为描述玩家之间的交互提供了新的视角，其中的误差将在设计 ZD 策略中发挥重要作用，吸引了各个领域的大量研究。本文探讨了在实现错误的情况下如何为多人双策略重复有限博弈设计 ZD 策略。首先，通过分解不同可能情况的概率来引入实现误差，并利用矩阵的半张量积（STP）构建策略过渡过程模型。其次，通过经典的 ZD 策略获取方法，提出了在实现误差下为多人双策略重复有限博弈设计 ZD 策略的步骤。然后，研究了在实现误差下检验 ZD 策略有效性的充分必要条件。此外，通过区分焦点玩家的邻居，将该方法扩展到实现误差下的网络进化博弈 （NEG） 进行群体决策，并提供了一种智能算法。最后，我们用两个例子来证明我们提出的方法的有效性。