It is an important decision-making problem for a miner in the blockchain networks if he/she participates in the mining so that he/she earns a reward by creating a new block earlier than other miners. We formulate this decision-making problem as a noncooperative game, because the probability of creating a block depends not only on one's own available computational resources, but also those of other miners. Through theoretical and numerical analyses, we show a hysteresis phenomenon of Nash equilibria depending on the reward and a jump phenomenon of miner decisions by a slight change in reward. We also show that the reward for which miners decide not to participate in the mining becomes smaller as the number of miners increases.

翻译：如果矿工参加采矿活动,从而比其他矿工早创造新的矿区,从而获得奖励,那么,就是一个重要决策问题。我们将这一决策问题作为一个不合作的游戏来表述,因为建立矿区的概率不仅取决于个人现有的计算资源,而且取决于其他矿工的计算资源。通过理论和数字分析,我们显示了纳什平衡的歇斯底里现象,取决于奖励和矿工决定的跳跃现象,因为报酬稍有变化。我们还表明,矿工决定不参加采矿的奖励随着矿工人数的增加而减少。