A Blockchain-Driven Stackelberg Game and MILP Algorithmic Framework for Dynamic Pricing in Multi-Agent Microgrid Networks

INTRODUCTION: Decentralized coordination and data transparency in multi-agent networks face significant computational and security bottlenecks when performing joint energy and ancillary service trading, particularly due to nonlinear optimization challenges in complex multi-domain environments. OBJECTIVES: This work aims to overcome these bottlenecks by developing an information-driven dynamic pricing framework that enables transparent, autonomous, and computationally efficient multi-agent decision-making. METHODS: The proposed framework integrates Ethereum-based smart contracts deployed on a public ledger to guarantee immutable data interactions and eliminate centralized dispatching. A Stackelberg game model is established to capture upper-lower level decision-making. To solve the resulting highly nonlinear and non-convex game exactly, the problem is transformed into a Mixed-Integer Linear Programming (MILP) model using Karush-Kuhn-Tucker (KKT) conditions and the duality theorem, ensuring exact convergence without approximation errors. RESULTS: Simulation results demonstrate the algorithm’s ability to efficiently find the exact Nash equilibrium, converging to a stable state in approximately 12 iterations. The KKT-MILP framework exhibits exceptional scalability, solving a 50-agent system within just 15 seconds and significantly outperforming traditional heuristic algorithms in computational latency. CONCLUSION: The proposed algorithmic framework mathematically ensures transparent and decentralized decision-making while substantially enhancing computational accuracy and overall economic efficiency of the multi-agent system.