Multi-Leader Multi-Follower Stackelberg Game in Mobile Blockchain Mining

The development of Blockchain-based mobile applications are impeded due to the resource limitations of mobile devices. Computation offloading can be a viable solution. In this paper, we consider a two-layer computation offloading paradigm including an edge computing service provider (ESP) and a cloud computing service provider (CSP). We formulate a multi-leader multi-follower Stackelberg game to address the computing resource management problem in such a network, by jointly maximizing the profits of each service provider (SP) and the payoffs of individual miners. We study two practical scenarios: a fixed-miner-number scenario for permissioned blockchains and a dynamic-miner-number scenario for permissionless blockchains. For the fixed-miner-number scenario, we discuss two different edge operation modes, i.e., the ESP is connected (to the CSP) or standalone, which form different miner subgames based on whether each miner's strategy set is mutually dependent. The existence and uniqueness of Stackelberg equilibrium (SE) in both modes are analyzed, according to which algorithms are proposed to achieve the corresponding SE(s). For the dynamic-miner-number scenario, we focus on the impact of population uncertainty and find that the uncertainty inflates the aggressiveness in the ESP resource purchasing. Numerical evaluations are presented to verify the proposed models.