Mining Pool Game Model and Nash Equilibrium Analysis for PoW-Based Blockchain Networks

Wenbai Li,Changbing Tang,Yue Wang,Mengwen Cao,Feilong Lin

doi:10.1109/access.2020.2997996

Abstract

Blockchain technology, has the characteristics of decentralization, openness and transparency, so that everyone can participate in database recording. Therefore, blockchain technology has a good application prospect in various industries. As the most successful application of blockchain technology, the Bitcoin system applies the Proof of Work (PoW) consensus mechanism. Under the PoW consensus mechanism, each miner competes through his own power to solve a SHA256 mathematical problem together, so as to gain profits. Due to the difficulty of the cryptography puzzle, miners tend to join the mining pool to obtain stable income. And the block withholding attacks will be carried out between the mining pools, so as to maximize his own income by controlling the infiltration rate dispatched to other mining pools. In this paper, we build a game model between mining pools based on the PoW consensus algorithm, and analyze its Nash equilibrium from two perspectives. The influence of the mining pools' power, the ratio of the power to be infiltrated, and the betrayed rate of dispatched miners on the mining pool's infiltration rate selection and income were explored, and the results were obtained through numerical simulations.

Highlights

Blockchain is a kind of chained data structure which combines data blocks in chronological order and ensures the tamper proof and forgery proof distributed ledger by cryptography
Let’s take M = 2 as an example, because here we only analyze the relationship between the system reward a and the mining pool to reach the Nash equilibrium, so the profit of the mining pool in the model obtained through the infiltrating power is temporarily represented by d
For existing papers, a mining pool game model based on the Proof of Work (PoW) consensus mechanism from the perspective of adding rewards and punishments to the blockchain system is builded firstly in this paper

Summary

INTRODUCTION

Blockchain is a kind of chained data structure which combines data blocks in chronological order and ensures the tamper proof and forgery proof distributed ledger by cryptography. Let’s take M = 2 as an example, because here we only analyze the relationship between the system reward a and the mining pool to reach the Nash equilibrium, so the profit of the mining pool in the model obtained through the infiltrating power is temporarily represented by d. According to the mixed strategy Nash equilibrium point, the mining pool chooses different strategies with the same expected return, which is: p2 + (1 − x)(a − d) = xd + p2 − ka + (1 − x)d , (8).

MODEL INTRODUCTION

SIMULATION

CONCLUSION