随机Stackelberg微分博弈视角下电商平台评论监管与商家激励策略研究

Study on E-Commerce Platform Comment Supervision and Merchant Incentive Strategies from the Perspective of Stochastic Stackelberg Differential Game

摘要: 为解决电商平台评论治理中监管与激励的动态适配问题，本文构建平台(领导者)-家(追随者)的线性二次随机Stackelberg微分博弈模型，以评论真实可信度为核心状态变量，引入布朗运动刻画市场不确定性，研究采用逆向归纳法结合随机哈密尔顿–雅可比–贝尔曼(HJB)方程推导均衡策略，系统分析核心参数与时域长度的调节效应，明确双方策略动态特性。结果表明：有限时域下，平台监管强度与商家激励强度均为评论可信度的线性反馈函数，呈现“时域约束 + 可信度驱动”双重动态特性，策略强度随剩余时间递减，前期重投入快速提升可信度，后期稳投入平衡成本与收益；成本收益系数、贴现因子、时域长度等核心参数对策略演化的调节作用显著，平台先动优势可通过监管策略引导商家激励行为，实现评论生态协同优化，且商家激励对可信度提升的主导效应更突出。

Abstract: To address the problem of dynamic adaptation between supervision and incentives in the comment governance of e-commerce platforms, this paper constructs a linear-quadratic stochastic Stackelberg differential game model with the platform as the leader and merchants as followers. Taking the authentic credibility of comments as the core state variable, Brownian motion is introduced to characterize market uncertainty. The equilibrium strategies are derived by adopting the backward induction method combined with the stochastic Hamilton-Jacobi-Bellman (HJB) equation. Meanwhile, the moderating effects of core parameters and time horizon length are systematically analyzed, and the dynamic characteristics of the strategies of both parties are clarified. The results show that: under a finite time horizon, both the platform’s supervision intensity and merchants’ incentive intensity are linear feedback functions of comment credibility, presenting the dual dynamic characteristics of “time horizon constraint + credibility-driven”. The intensity of strategies decreases with the remaining time, indicating that heavy investment in the early stage can rapidly improve credibility, while steady investment in the later stage balances costs and benefits. Core parameters such as cost-benefit coefficients, discount factors, and time horizon length exert significant moderating effects on strategy evolution. The platform’s first-mover advantage can guide merchants’ incentive behaviors through supervision strategies, thereby achieving the collaborative optimization of the comment ecosystem. Moreover, merchants’ incentives play a more prominent leading role in improving credibility.