Evolutionary Equilibrium Analysis for Decision on Block Size in Blockchain Systems

In a PoW-based blockchain network, mining pools (the solo miner could be regarded as pool containing one miner) compete to successfully mine blocks pursue rewards. Generally, the rewards include fixed block subsidies and time-varying transaction fees. The fees are offered by senders whose transactions packaged into is increasing with size. However, larger size of brings longer latency, resulting in smaller probability mining. Therefore, finding optimal trade off these two factors complex crucial problem for pools. this paper, we model repeated competition dynamics system an evolutionary game study interactions among game, each has strategies: follow default $\bar{B}$, i.e., upper bound size, or not follow. Because bounded rationality, pursues its stable (ESS) according pools' computing power other continuous learning adjustments during whole process. A framework built general based on which then theoretically explore existence stability ESSs case Numerical experiments real Bitcoin data conducted show decisions demonstrate theoretical findings paper.