Decision on block size in blockchain systems by evolutionary equilibrium analysis

Abstract

By using the PoW protocol, mining pools compete to successfully mine blocks to pursue rewards. Generally, the reward from a mined block includes the fixed block subsidies and the time-varying transaction fees. The latter are offered by the senders whose transactions are packaged into blocks and are increasing with the block size being larger. However, the larger block size brings the longer latency, resulting in a smaller probability of successfully mining. Therefore, decision on the optimal block size of a block to trade off two factors above mentioned is a complex and crucial problem for the mining pools. In this paper, we model the repeated mining competition dynamics among mining pools as an evolutionary game, in which each mining pool has two strategies: following the upper bound of block size B¯, or selecting a block size smaller than B¯. Because of the bounded rationality, each mining pool pursues its evolutionary stable strategy (ESS) on block size by continuous learning and adjustments during the whole mining process. A framework is built for the general evolutionary game, based on which we then explore the existence and stability of the ESSs for a case of two mining pools. Numerical experiments using the real Bitcoin data are conducted to demonstrate the theoretical results in this paper.