From Griefing to Stability in Blockchain Mining Economies

TL;DR

This paper models blockchain mining economies, showing how griefing affects stability and how larger networks tend to stabilize through market-like dynamics, with empirical evidence from cryptocurrency case studies.

Contribution

It introduces a game-theoretic model of griefing in blockchain mining and proposes a proportional response protocol that ensures convergence to stable market equilibria.

Findings

Griefing is prevalent at Nash equilibria in small networks.

Market-like dynamics emerge as networks grow, reducing griefing impact.

Empirical case studies support the role of risk diversification and resource mobility in stability.

Abstract

We study a game-theoretic model of blockchain mining economies and show that griefing, a practice according to which participants harm other participants at some lesser cost to themselves, is a prevalent threat at its Nash equilibria. The proof relies on a generalization of evolutionary stability to non-homogeneous populations via griefing factors (ratios that measure network losses relative to deviator's own losses) which leads to a formal theoretical argument for the dissipation of resources, consolidation of power and high entry barriers that are currently observed in practice. A critical assumption in this type of analysis is that miners' decisions have significant influence in aggregate network outcomes (such as network hashrate). However, as networks grow larger, the miner's interaction more closely resembles a distributed production economy or Fisher market and its stability properties change. In this case, we derive a proportional response (PR) update protocol which converges to market equilibria at which griefing is irrelevant. Convergence holds for a wide range of miners risk profiles and various degrees of resource mobility between blockchains with different mining technologies. Our empirical findings in a case study with four mineable cryptocurrencies suggest that risk diversification, restricted mobility of resources (as enforced by different mining technologies) and network growth, all are contributing factors to the stability of the inherently volatile blockchain ecosystem.