  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 that all miners
participate in the mining. Numerical simulation shows that there is a trade-off
in the choice of the design parameters.
