An Overlapping Coalition Game Approach for Collaborative Block Mining and Edge Task Offloading in MEC-assisted Blockchain Networks

Mobile edge computing (MEC) is a promising technology that enhances the efficiency of mobile blockchain networks, by enabling miners, often acted by mobile users (MUs) with limited computing resources, to offload resource-intensive mining tasks to nearby edge computing servers. Collaborative block mining can further boost mining efficiency by allowing multiple miners to form coalitions, pooling their computing resources and transaction data together to mine new blocks collaboratively. Therefore, an MEC-assisted collaborative blockchain network can leverage the strengths of both technologies, offering improved efficiency, security, and scalability for blockchain systems. While existing research in this area has mainly focused on the singlecoalition collaboration mode, where each miner can only join one coalition, this work explores a more comprehensive multicoalition collaboration mode, which allows each miner to join multiple coalitions. To analyze the behavior of miners and the edge computing service provider (ECP) in this scenario, we propose a novel two-stage Stackelberg game. In Stage I, the ECP, as the leader, determines the prices of computing resources for all MUs. In Stage II, each MU decides the coalitions to join, resulting in an overlapping coalition formation (OCF) game; Subsequently, each coalition decides how many edge computing resources to purchase from the ECP, leading to an edge resource competition (ERC) game. We derive the closed-form Nash equilibrium for the ERC game, based on which we further propose an OCFbased alternating algorithm to achieve a stable coalition structure for the OCF game and develop a near-optimal pricing strategy for the ECP's resource pricing problem. Simulation results show that the proposed multi-coalition collaboration mode can improve the system efficiency by 12.64% ∼ 17.63%, compared to the traditional single-coalition collaboration mode.