Proof-of-Stake Mining Games with Perfect Randomness. Ferreira, M. V. X. & Weinberg, S. M. In Proceedings of the 22nd ACM Conference on Economics and Computation, of EC '21, pages 433–453, New York, NY, USA, 2021. Association for Computing Machinery.
Proof-of-Stake Mining Games with Perfect Randomness [link]Paper  Proof-of-Stake Mining Games with Perfect Randomness [link]Video  doi  abstract   bibtex   155 downloads  
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. 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 32.8% of the total stake. Note that a miner of this size 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 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.
@inproceedings{ferreira2021pos,
  author = {Ferreira, Matheus V. X. and Weinberg, S. Matthew},
  title = {Proof-of-Stake Mining Games with Perfect Randomness},
  year = {2021},
  isbn = {9781450385541},
  publisher = {Association for Computing Machinery},
  address = {New York, NY, USA},
  url = {https://arxiv.org/abs/2107.04069},
  doi = {10.1145/3465456.3467636},
  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. 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 32.8% of the total stake. Note that a miner of this size 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 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.},
  booktitle = {Proceedings of the 22nd ACM Conference on Economics and Computation},
  pages = {433–453},
  numpages = {21},
  keywords = {proof-of-stake blockchains, energy-efficiency, NASH equilibrium, cryptocurrency, random beacons},
  location = {Budapest, Hungary},
  series = {EC '21},
  url_Video = {https://www.youtube.com/watch?v=ZSq8-YSWGrk}
}

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