Insightful Mining Equilibria

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 novel strategy called insightful mining to counteract the selfish mining attack. 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 is strictly greater than the selfish pool’s when they have the same mining power. Then we investigate the mining game where all pools can choose to be honest or take the insightful mining strategy. We characterize the Nash equilibrium of such a game and derive three corollaries: (a) each mining game has a pure Nash equilibrium; (b) there are at most two insightful pools under some equilibrium no matter how the mining power is distributed; (c) honest mining is a Nash equilibrium if the largest mining pool has a fraction of mining power no more than 1/3. Our work explores, for the first time, the idea of spying in the selfish mining attack, which might shed new light on researchers in the field.