This article focuses on the transformation and development of traditional industries in the context of digital economy. The Hamilton-Jacobi-Berman equation is used to investigate the coordination mechanism and optimal strategy of industrial integration from a quantitative perspective and examine the dynamic decision-making processes among traditional enterprises, digital technology providers, and local governments by constructing a tripartite dynamic differential game model, and the degree of optimal effort, the optimal benefits, the level of industrial digitalization and the proportion of local government subsidies to enterprises are obtained in three cases: a Nash non-cooperative game, a Stackelberg game and a cooperative game. The results show that (1) the government subsidy coefficient, as an effective adjustment mechanism, can significantly improve the degree of optimal effort of traditional enterprises and digital technology providers, (2) the tripartite optimal strategy, optimal benefits, total system benefits and level of industrial digitization in the case of the cooperative game are strictly superior to those in non-cooperative situations, achieving the Pareto optimum of the system, (3) the results of the theoretical derivation are verified through the analysis of numerical simulation and case study. The study provides a theoretical basis and practical support for the digital transformation of traditional industries.

本文着眼于数字经济背景下传统产业的转型与发展。利用Hamilton-Jacobi-Berman方程从定量角度研究产业整合的协调机制和最优策略，通过构建三方动态微分博弈考察传统企业、数字技术提供商和地方政府之间的动态决策过程模型，在纳什非合作博弈、斯塔克尔伯格博弈和合作博弈三种情况下得到最优努力程度、最优收益、产业数字化水平和地方政府对企业的补贴比例。结果表明，（1）政府补贴系数作为一种有效的调节机制，可以显着提高传统企业和数字技术提供商的最优努力程度，（2）合作博弈情况下的三方最优策略、最优收益、总系统收益和产业数字化水平严格优于非合作博弈中的三方最优策略、最优收益、总系统收益和产业数字化水平。 (3)通过数值模拟和案例分析验证了理论推导的结果。该研究为传统产业的数字化转型提供了理论依据和实践支撑。合作博弈情况下的系统总收益和产业数字化水平严格优于非合作情况，达到系统的帕累托最优，(3)通过数值分析验证了理论推导的结果模拟和案例研究。该研究为传统产业的数字化转型提供了理论依据和实践支撑。在合作博弈的情况下，系统总收益和工业数字化水平严格优于非合作情况，从而实现了系统的帕累托最优；（3）通过数值分析验证了理论推导的结果模拟和案例研究。该研究为传统产业的数字化转型提供了理论依据和实践支撑。