Proof-of-Stake Mining Games with Perfect Randomness

TL;DR

This paper analyzes the incentives and security of Proof-of-Stake blockchains with perfect randomness, showing that strategic miners can outperform honest miners at certain stake levels, but security can be approximately achieved with enough stake.

Contribution

It introduces a formal model of Proof-of-Stake mining with perfect randomness, characterizes optimal strategies, and compares incentive security to Proof-of-Work protocols.

Findings

A miner with 32.5% stake can outperform honest miners, unlike in Proof-of-Work.

A miner with 30.8% stake cannot outperform honest miners, indicating near-PoW security.

The strategy space in PoS mining is richer and admits an optimal positive recurrent strategy.

Abstract

Proof-of-Stake blockchains based on a longest-chain consensus protocol are an attractive energy-friendly alternative to the Proof-of-Work paradigm. However, formal barriers to "getting the incentives right" were recently discovered, driven by the desire to use the blockchain itself as a source of pseudorandomness \cite{brown2019formal}. We consider instead a longest-chain Proof-of-Stake protocol with perfect, trusted, external randomness (e.g. a randomness beacon). We produce two main results. First, we show that a strategic miner can strictly outperform an honest miner with just $32.5\%$ of the total stake. Note that a miner of this size {\em cannot} outperform an honest miner in the Proof-of-Work model. This establishes that even with access to a perfect randomness beacon, incentives in Proof-of-Work and Proof-of-Stake longest-chain protocols are fundamentally different. Second, we prove that a strategic miner cannot outperform an honest miner with $30.8\%$ of the total stake. This means that, while not quite as secure as the Proof-of-Work regime, desirable incentive properties of Proof-of-Work longest-chain protocols can be approximately recovered via Proof-of-Stake with a perfect randomness beacon. The space of possible strategies in a Proof-of-Stake mining game is {\em significantly} richer than in a Proof-of-Work game. Our main technical contribution is a characterization of potentially optimal strategies for a strategic miner, and in particular, a proof that the corresponding infinite-state MDP admits an optimal strategy that is positive recurrent.