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.

翻译：为确保安全,维持以铁链为基础的服务,这是一个重要问题,如何决定采矿奖励,使参与采矿的矿工人数增加。我们提出一个动态决策模式,采用渐进式游戏方法,分析拟议模式平衡点的稳定性。提议的模型用第一级差异方程式描述。因此,它很简单,但其理论分析使人能洞察到决策的特征。通过对平衡点的分析,我们展示平衡点的跨临界裂缝和歇斯底里现象。我们还设计一个控制器,根据参与采矿的矿工人数确定采矿奖励,以稳定所有矿工参与采矿的状态。数字模拟显示,在选择设计参数时存在权衡。