Abstract: It is agreed that the digital economy will bring subversive innovation to businesses and organizations, and stimulate the needs of enterprise digital transformation and endogenous power. However, due to the variety of the traditional enterprise products, the diversity of the user data and the differentiation of ability development, it is difficult to achieve digital upgrade in a short period of time. Fortunately, the digital technologies such as cloud computing provide an important technical support for the digital transformation of enterprises. In particular, the cloud-edge collaboration technology can provide faster business processing ability and better user service quality, thus attracting extensive attention from scholars and entrepreneurs from all fields. However, for the academic community, many scholars have studied more from the technical optimization perspective of computing offloading, task and resource scheduling, and resource allocation, and less on the inherent law of game behavior between digital technology enterprises which are mainly regarded as two parties: cloud service providers and edge operators.
Under the bounded rationality assumption, this article presents a dynamic evolution game model between cloud service providers and edge operators for the edge-cloud framework according to the evolutionary game theory, explores the unilateral evolutionary stability strategies under four different conditions based on the stability theorem for differential equations, and analyzes the evolution path of each player and the influence affected by the other’s strategy choice in the actual cases. The equilibrium of the system is calculated according to the replicated dynamic equations, and the Jacobian matrix is also constructed. In accordance with the criterion proposed by Friedman, the equilibrium is proven to be an evolutionary stability strategy under different conditions, and the combination of evolutionary stability equilibria under different conditions is also obtained. The evolution law of the system is analyzed and the evolution results are classified and summarized. Then the basic conditions for achieving the cloud-edge cooperative relationship are found. Furthermore, this article also investigates the influence factors of stable cooperative relationship between cloud service providers and edge operators in two kinds of evolutionary stability strategies, and verifies the theoretical analysis results through numerical simulation results.
The research results show that the final evolution of the cloud-edge collaboration system depends on the benefits and costs of the game matrix between the two parties as well as the system initial state values. The two parties will finally reach a stable cloud-edge collaborative relationship after continuous learning and adjustment of strategies in a long time enough, when the cost of constrained loss is at least greater than the difference between the benefit of both parties choosing to deal alone and the benefit of their cooperative treatment. The distribution coefficient of revenue and cost has different effects on the cooperative evolution of the system with different conditions, and needs to be adjusted dynamically in a real time according to market changes. The lower the risk coefficient of cloud edge collaborative processing for both parties, that is, the higher the safety coefficient, the more conducive to the construction of the cloud-edge collaboration system. Under a certain condition, the cloud-edge collaboration system can be eventually driven to be an ideal state by reducing the collaboration cost and improving the collaboration revenue, so as to effectively promote the long-term stability of cloud-edge collaboration system and better serve the enterprise digital transformation.

Key words: digital economy, digital transformation, cloud-edge collaboration, evolutionary game

摘要： 在数字经济日新月异的时代背景下,云边协同为企业数字化转型提供了更高效、灵活、可靠的技术解决方案,受到了学界及业界的广泛关注。本文基于云边架构和演化博弈理论构建云边博弈模型,分析双方在各情形下的演化稳定策略,并针对存在两种演化稳定策略的情形,进一步分析影响其协同关系稳定的因素,最后通过数值仿真验证理论分析结果。研究表明,云边协同系统的最终演化方向取决于支付矩阵中各变量之间的关系,当系统存在多种演化结果时,初始状态会对演化结果产生重要影响,通过合理调整相关变量可以有效激励系统演化为理想状态,从而促进云边协同系统的长期稳定,更好地服务于企业数字化转型。

关键词: 数字经济, 数字化转型, 云边协同, 演化博弈