分段惩罚机制的广义N人演化雪堆博弈模型在电子商务平台中的应用

The Application of Generalized N-Person Evolutionary Snowdrift Game Model with Segmented Penalty Mechanism in E-Commerce Platform

摘要: 在传统的雪堆博弈中，通常假设对所有背叛者施加惩罚。然而，在实际的市场营销环境中，企业的惩罚预算通常是有限的，因此考虑随机选择一定比例的背叛顾客进行惩罚显得尤为重要。在此背景下，我们探讨将分段惩罚机制引入多人雪堆博弈模型，重点分析其对合作演化的影响。我们的目的是研究分段惩罚机制在雪堆博弈中的应用，分析均衡点的确定性稳定和随机稳定。研究结果表明，在确定性情况下，无论是二人还是多人雪堆博弈中，合作者的比例随着惩罚比例的增加而提高，从而更有效地促进市场中的合作与品牌忠诚。这一发现为企业设计灵活的惩罚策略提供了理论支持，有助于在资源受限的情况下优化客户关系管理，提升电子商务平台的信任度和用户满意度。

Abstract: In the traditional snowdrift game, it is usually assumed that all betrayers are punished. However, in the actual marketing environment, the punishment budget of enterprises is usually limited, so it is particularly important to consider randomly selecting a certain proportion of betrayed customers for punishment. In this context, we explore the introduction of the segmented punishment mechanism into the multi-person snowdrift game model, focusing on its impact on the evolution of cooperation. Our purpose is to study the application of piecewise penalty mechanism in snowdrift game, and analyze the deterministic stability and stochastic stability of the equilibrium point. The results show that in the deterministic case, whether it is a two-person or multi-person snowdrift game, the proportion of collaborators increases with the increase of the penalty ratio, thus more effectively promoting cooperation and brand loyalty in the market. This finding provides theoretical support for enterprises to design flexible punishment strategies, helps to optimize customer relationship management in resource-constrained situations, and improves the trust and user satisfaction of e-commerce platforms.