On Game-theoretic Computation Power Diversification in the Bitcoin Mining Network

Abstract

In the Bitcoin mining network, miners contribute computation power to solve crypto-puzzles in exchange for financial rewards. Due to the randomness and the competitiveness of mining, individual miners tend to join mining pools for low risks and steady incomes. Usually, a pool is managed by its central operator, who charges fees for providing risk-sharing services. This paper presents a hierarchical distributed computation paradigm where miners can distribute their power among multiple pools. By adding virtual pools, we separate miners’ dual roles of being the operator as well as being the member when solo mining. We formulate a multi-leader multi-follower Stackelberg game to study the joint utility maximization of pool operators and miners, thereby addressing a computation power allocation problem. We investigate two practical pool operation modes, a uniform-share-difficulty mode and a nonuniform-share-difficulty mode. We derive analytical results for the Stackelberg equilibrium of the game under both modes, based on which optimal strategies are designed for all operators and miners. Numerical evaluations are presented to verify the proposed model.