Stackelberg Game Based Resource Pricing and Scheduling in Edge-Assisted Blockchain Networks

Abstract

Currently, the blockchain, as a key enabling technology of digital currency, has attracted lots of attention from both industry and academia. The blockchain mining process requires high computing power to solve a Proof-of-Work (PoW) puzzle, which is hard to implement on users' mobile devices. So these miners may leverage the resources of the edge/cloud service providers (ESPs/CSP) to calculate the PoW puzzle. The existing edge-assisted blockchain networks simply assumed that all ESPs have a uniform propagation delay, which is not realistic. In this paper, we consider a more practical scene where ESPs with distributed geographic locations have diverse propagation delays when supporting the computation of the PoW puzzle. Additionally, the blockchain mining process generally involves the complicated competition and game among these ESPs and miners. Each ESP focuses on how to determine his resource price and to select the requests from the miners, so that he can maximize his utility. According to the set resource price, each miner concentrates on scheduling his resource requests for each ESP to maximize his individual utility which depends on ESPs' resource price and propagation delays. We model such a resource pricing and scheduling problem as a multi-leader multi-follower Stackelberg game and aim at finding the joint maximization of the utilities of each ESP and each individual miner. We prove the existence and uniqueness of the Stackelberg equilibrium (SE) and meanwhile propose an algorithm to achieve the corresponding SE. Finally, extensive simulations are conducted to verify the significant performance of the proposed solution.