ProofofStake Mining Games with Perfect Randomness
Abstract
ProofofStake blockchains based on a longestchain consensus protocol are an attractive energyfriendly alternative to the ProofofWork 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 longestchain ProofofStake 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 ProofofWork model. This establishes that even with access to a perfect randomness beacon, incentives in ProofofWork and ProofofStake longestchain 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 ProofofWork regime, desirable incentive properties of ProofofWork longestchain protocols can be approximately recovered via ProofofStake with a perfect randomness beacon. The space of possible strategies in a ProofofStake mining game is {\em significantly} richer than in a ProofofWork game. Our main technical contribution is a characterization of potentially optimal strategies for a strategic miner, and in particular, a proof that the corresponding infinitestate MDP admits an optimal strategy that is positive recurrent.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.04069
 Bibcode:
 2021arXiv210704069F
 Keywords:

 Computer Science  Computer Science and Game Theory;
 Computer Science  Cryptography and Security;
 Economics  Theoretical Economics
 EPrint:
 79 Pages, ACM EC 2021