具有完美随机性的权益证明挖矿博弈
Proof-of-Stake Mining Games with Perfect Randomness
AI总结：
本文研究具有完美外部随机性的最长链权益证明协议中的矿工激励问题，证明策略性矿工在32.5%权益时可优于诚实矿工但在30.8%时不能，并刻画了无限状态MDP的正递归最优策略。
摘要：
基于最长链共识协议的权益证明区块链是工作量证明范式的一种有吸引力的节能替代方案。然而，由于希望将区块链本身用作伪随机性来源，最近发现了“正确设置激励”的形式化障碍。我们转而考虑一种具有完美、可信、外部随机性（例如随机信标）的最长链权益证明协议。我们得到两个主要结果。首先，我们证明一个策略性矿工仅凭总权益的32.5%就能严格优于诚实矿工。注意，这种规模的矿工在工作量证明模型中无法优于诚实矿工。这表明即使能够访问完美的随机信标，工作量证明和权益证明最长链协议中的激励在根本上也是不同的。其次，我们证明一个策略性矿工凭借总权益的30.8%无法优于诚实矿工。这意味着，虽然不如工作量证明机制那么安全，但工作量证明最长链协议所期望的激励性质可以通过具有完美随机信标的权益证明近似恢复。权益证明挖矿博弈中可能策略的空间比工作量证明博弈显著更丰富。我们的主要技术贡献是对策略性矿工潜在最优策略的刻画，特别是证明了相应的无限状态MDP存在一个正递归的最优策略。
英文摘要：
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.
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