Cloud/Fog Computing Resource Management and Pricing for Blockchain Networks

Public blockchain networks using proof of work-based consensus protocols are considered a promising platform for decentralized resource management with financial incentive mechanisms. In order to maintain a secured, universal state of the blockchain, proof of work-based consensus protocols financially incentivize the nodes in the network to compete for the privilege of block generation through cryptographic puzzle solving. For rational consensus nodes, i.e., miners with limited local computational resources, offloading the computation load for proof of work to the cloud/fog providers becomes a viable option. In this paper, we study the interaction between the cloud/fog providers and the miners in a proof of work-based blockchain network using a game theoretic approach. In particular, we propose a lightweight infrastructure of the proof of work-based blockchains, where the computation-intensive part of the consensus process is offloaded to the cloud/fog. We formulate the computation resource management in the blockchain consensus process as a two-stage Stackelberg game, where the profit of the cloud/fog provider and the utilities of the individual miners are jointly optimized. In the first stage of the game, the cloud/fog provider sets the price of offered computing resource. In the second stage, the miners decide on the amount of service to purchase accordingly. We apply backward induction to analyze the sub-game perfect equilibria in each stage for both uniform and discriminatory pricing schemes. For uniform pricing where the same price applies to all miners, the uniqueness of the Stackelberg equilibrium is validated by identifying the best response strategies of the miners. For discriminatory pricing where the different prices are applied, the uniqueness of the Stackelberg equilibrium is proved by capitalizing on the variational inequality theory. Further, the real experimental results are employed to justify our proposed model.