Blockchain is a distributed ledger technology for recording transactions. When two or more miners create different versions of the blocks at almost the same time, blockchain forks occur. We model the mining process with forks by a discrete event system and design a supervisor controlling these forks.

To maintain blockchain-based services with ensuring its security, it is an important issue how to decide a mining reward so that the number of miners participating in the mining increases. We propose a dynamical model of decision-making for miners using an evolutionary game approach and analyze the stability of equilibrium points of the proposed model. The proposed model is described by the 1st-order differential equation. So, it is simple but its theoretical analysis gives an insight into the characteristics of the decision-making. Through the analysis of the equilibrium points, we show the transcritical bifurcations and hysteresis phenomena of the equilibrium points. We also design a controller that determines the mining reward based on the number of participating miners to stabilize the state where all miners participate in the mining. Numerical simulation shows that there is a trade-off in the choice of the design parameters.