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.

中文翻译：

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区块链挖矿决策问题的博弈论方法


对于区块链网络中的矿工来说，如果他/她参与挖矿以便比其他矿工更早创建新区块来获得奖励，这是一个重要的决策问题。我们将这个决策问题表述为非合作博弈，因为创建区块的概率不仅取决于自己可用的计算资源，还取决于其他矿工的计算资源。通过理论和数值分析，我们展示了纳什均衡依赖于奖励的滞后现象和矿工决策因奖励的微小变化而出现的跳跃现象。我们还表明，随着矿工数量的增加，矿工决定不参与挖矿的奖励会变小。