Industrial digital transformation strategies based on differential games

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.