关键词: 量子博弈, 共识决策, 社交网络, 公平关切

Abstract: Group consensus decision-making is a process of collecting and integrating the opinions of each individual in a group through effective communication, negotiation, and discussion in order to reach a consensus and make a decision. The game consensus decision-making model has received widespread attention because it takes into account the opinions and coordination of all individuals, which can effectively solve the consensus-reaching problem with large differences in opinions. However, the existing game consensus decision-making models have several drawbacks, such as the assumption that individuals are completely independent and cognitively rational. In fact, an individual is often influenced and interfered with by the opinions of other individuals in decision-making, forming a kind of entanglement effect. Specifically, before making a final decision, an individual’s consciousness will be disrupted by the superposition of different external ideas, resulting in a “superposition state”. They will not be expressed externally as a specific action strategy until a final choice is made. During this process, an individual’s psychology and behavior will contradict the “principle of certainty” and the “law of total probability”, resulting in the individual’s inability to make decisions independently, which in turn affects the effectiveness and quality of consensus. In addition, the existing game consensus decision-making models ignore the fairness perceptions of the individuals. In many real-world decision-making problems, an individual prefers to compare the benefits he obtains with those another does, generating a perception of fairness of the decision options. This may also influence the subsequent decision-making behavior.
Based on the above discussion, in order to more accurately simulate the group consensus process, this paper proposes a quantum game consensus model based on social network fairness. We design the objective function considering the entanglement and fairness concerns in the interests of the coordinator and decision maker. Among them, an objective function to minimize the total consensus cost and the difference between individual and group opinions is designed for coordinators, and an objective function to maximize financial compensation and satisfaction is designed for each decision-maker. Based on this, we establish the quantum game model for both sides and analyze the existence of a quantum equilibrium strategy. Then, a quantum game consensus optimization model is constructed with the objective of minimum cost for coordinators, and the solution set containing the proposed opinion, adjustment opinion, and unit adjustment cost can be obtained.
To evaluate the accuracy and practicality of the proposed model, the application scenario of the model is illustrated by taking the development of coordination contracts for a new energy vehicle supply chain as an example. In addition, a sensitivity and comparative analysis of the model in this paper is performed to verify the validity of the model. The results show that the quantum game consensus model broadens the game’s strategy space and improves the game consensus efficiency. It also implies that the proposal can accurately simulate the individual’s irrational cognitive decision-making process. The research findings of this study can, on the one hand, assist coordinators in precisely identifying decision makers’ social network fairness in decision-making behaviors, increase decision-making accuracy, and better facilitate group consensus. On the other hand, it assists decision-makers in actively participating in the group consensus process, reducing the danger of information asymmetry, maintaining market order, and improving the game consensus benefits of the participants.
There are still certain areas where we may make improvements in the future. For instance, the coordinator can apply asymmetric unit coordination costs because it has inconsistent subsidy preferences for the direction of decision-maker opinion alteration. In addition, there are ambiguous trust relationships among decision-makers. It is also necessary to pay close attention to how to employ quantum probability to depict the interference effect between numerous trust sources and better describe the degree of interconnectedness between nodes.

Key words: quantum game, consensus decision-making, social networks, fairness concern