On Block Size Value in Proof-of-Work Blockchains With Zero Block Reward

According to the Bitcoin blockchain protocol, the block reward will decrease to zero over time, leaving miners to rely solely on transaction fees for their income. Consequently, elevating the block size translates into augmented rewards for the successful miner. However, counterbalancing this, network latency reduces the miner’s probability of success when the block size increases. Choosing the suitable block size is crucial for maximizing profit and can significantly influence the network’s stability and robustness. This paper focuses on the problem of selecting the most optimal block size under the given circumstances. Through the utilization of win probability and the computation of miners’ expected profits, we demonstrate that each miner possesses an optimal and distinct block size considering the block size and mining power of fellow miners. Furthermore, we determine and elucidate the Nash equilibrium in the miners’ game. In this Nash equilibrium, miners with higher mining power will choose larger block sizes, and the miner with the greatest mining power can independently determine their block size without considering other miners. Also, when all miners have equal mining power, they will unanimously select the same block size. We have additionally analyzed the scenario where the block size is restricted. In this case, we have identified the best response and Nash equilibrium, demonstrating that miners choose the maximum feasible block size under specific conditions. Moreover, it has been established that if the block size surpasses a certain threshold, none of the miners will select the maximum block size. Conversely, if the block size falls below a threshold, all miners will choose the maximum block size value.