Distributionally Robust Game for Proof-of-Work Blockchain Mining Under Resource Uncertainties

Blockchain plays a crucial role in ensuring the security and integrity of decentralized systems, with the proof-of-work (PoW) mechanism being fundamental for achieving distributed consensus. As PoW blockchains see broader adoption, an increasingly diverse set of miners with varying computing capabilities participate in the network. In this paper, we consider the PoW blockchain mining, where the miners are associated with resource uncertainties. To characterize the uncertainty computing resources at different mining participants, we establish an ambiguous set representing uncertainty of resource distributions. Then, the networked mining is formulated as a non-cooperative game, where distributionally robust performance is calculated for each individual miner to tackle the resource uncertainties. We prove the existence of the equilibrium of the distributionally robust mining game. To derive the equilibrium, we propose the conditional value-at-risk (CVaR)-based reinterpretation of the best response of each miner. We then solve the individual strategy with alternating optimization, which facilitates the iteration among miners towards the game equilibrium. Furthermore, we consider the case that the ambiguity of resource distribution reduces to Gaussian distribution and the case that another uncertainties vanish, and then characterize the properties of the equilibrium therein along with a distributed algorithm to achieve the equilibrium. Simulation results show that the proposed approaches effectively converge to the equilibrium, and effectively tackle the uncertainties in blockchain mining to achieve a robust performance guarantee.