A Multi-Leader Multi-Follower Game-Theoretic Approach for Delay-constrained Mining Task Offloading in MEC-assisted Blockchain Networks

Blockchain is a decentralized and secure digital ledger system that ensures data integrity through immutable records and cryptographic consensus mechanisms. However, in mobile blockchain networks, the computation-intensive proof-of-work (PoW) mining process often imposes a significant burden on mobile users (MUs) who serve as miners, particularly given their limited computing resources. Mobile edge computing (MEC) offers a promising solution to alleviate the burden on MUs, by enabling them to offload their mining tasks to nearby edge servers. While existing studies have explored MEC-assisted blockchain networks in both single-server and multi-server scenarios, they often overlook crucial aspects of blockchain networks, such as the transmission and computation delays inherent in the mining process. In this work, we investigate a more realistic MEC-assisted mobile blockchain network, where mining tasks are explicitly modeled with delay constraints to better capture real-world performance challenges. To analyze the strategic interactions between MUs and edge computing service providers (ECPs), we formulate a two-stage multi-leader and multi-follower Stackelberg game, which consists of an ECP Resource Pricing (ERP) game at Stage I, and an MU Resource Competition (MRC) game at Stage II. Specifically, in the ERP game at Stage I, ECPs, acting as leaders, set the resource prices for MUs; and in the MRC game at Stage II, MUs, acting as followers, determine their computing resource demands based on the prices of ECPs. We first prove the existence of Nash equilibrium (NE) for both games, and then derive the closed-form conditions for the NE of the MRC game at Stage II. Based on the above, we further propose a sub-gradient-based resource pricing algorithm that can converge to the NE of the ERP game at Stage I. Simulation results show that, when compared to the centralized cooperative solution, our proposed non-cooperative game approach can significantly reduce the computational complexity, while incurring only a modest performance degradation, e.g., the social welfare loss ranges from 6.64% to 9.96%.