Insightful Mining Equilibria

TL;DR

This paper introduces insightful mining as a counter-strategy to selfish mining in blockchain, analyzes its effectiveness, and characterizes the Nash equilibria in multi-agent mining games, showing conditions under which honest mining prevails.

Contribution

It proposes insightful mining, a novel strategy to resist selfish mining, and provides a comprehensive equilibrium analysis of mining behaviors in blockchain systems.

Findings

Insightful mining can outperform selfish pools with equal mining power.

Pure Nash equilibria exist in the mining game.

Honest mining is stable if the largest pool has at most 1/3 of total power.

Abstract

The selfish mining attack, arguably the most famous game-theoretic attack in blockchain, indicates that the Bitcoin protocol is not incentive-compatible. Most subsequent works mainly focus on strengthening the selfish mining strategy, thus enabling a single strategic agent more likely to deviate. In sharp contrast, little attention has been paid to the resistant behavior against the selfish mining attack, let alone further equilibrium analysis for miners and mining pools in the blockchain as a multi-agent system. In this paper, first, we propose a strategy called insightful mining to counteract selfish mining. By infiltrating an undercover miner into the selfish pool, the insightful pool could acquire the number of its hidden blocks. We prove that, with this extra insight, the utility of the insightful pool could be strictly greater than the selfish pool's when they have the same mining power. Then we investigate the mining game where all pools can either choose to be honest or take the insightful mining strategy. We characterize the Nash equilibrium of this mining game, and derive three corollaries: (a) each mining game has a pure Nash equilibrium; (b) honest mining is a Nash equilibrium if the largest mining pool has a fraction of mining power no more than 1/3; (c) there are at most two insightful pools under equilibrium no matter how the mining power is distributed.