Game-theoric approach to decision-making problem for blockchain mining

It is an important decision-making problem for a miner in blockchain networks if he/she does the mining so that he/she earns a reward by creating a new block earlier than the other miners. We formulate the decision-making problem as a non-cooperative game because the probability of creating blocks depends on not only his/her own computational resource but also other miners' computational resources. By the theoretical and numerical analysis, we show a hysteresis phenomenon of Nash equilibria depending on the reward and a jump phenomenon of the decision of the miners by a slight change of the reward. We also show that the reward for which miners decide to quit mining becomes smaller as the number of miners increases.