Stability analysis and control of decision-making of miners in blockchain

TL;DR

This paper models miners' decision-making in blockchain using an evolutionary game approach, analyzing stability and bifurcations to inform reward strategies that promote widespread participation.

Contribution

It introduces a simple dynamical model for miners' decisions and provides stability analysis, including bifurcation and hysteresis phenomena, to guide reward design.

Findings

Identification of transcritical bifurcations in miners' participation dynamics

Design of a controller for stable, full participation in mining

Numerical simulations reveal trade-offs in reward parameter choices

Abstract

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.