Game-based Intelligent Optimization for Pricing of Duopoly Industrial Supply Chains based on Two-level Gradient Equilibrium Algorithm

Recently, intelligent computation algorithms have been extended into every field, and the trend of digitization and intelligence in the decision-making system of supply chain management is becoming more and more obvious. In this article, the pricing intelligent optimization management for the duopoly supply chains is considered and the optimal pricing model based on the Stackelberg-Nash equilibrium model is constructed. The corresponding autonomous two-level gradient-based equilibrium algorithm for the pricing management systems is designed to analyze the modeling characteristics of the pricing optimal model with the simulation results. Firstly, the profit models of the retailers and manufacturers are given by analyzing the demand and occurred costs for the duopoly supply chain systems. Based on the above models, the optimal pricing strategy based on the Stackelberg-Nash game are constructed and the corresponding Nash equilibrium (NE) points for the optimal pricing are obtained according to the profit models. Furthermore, the novel two-level gradient-based algorithm for the pricing management systems is designed to obtain the optimal equilibrium points of the unit retail price, unit wholesale price, and length of the replenishment cycle. Finally, the designed gradient-based algorithm is implemented through the simulation, and the optimization characteristics of the game-based optimal model are analyzed. The NE-based optimal prices and the convergence of the proposed algorithm for retailers and manufacturers are illustrated by the simulation results.