  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.
