Proof-of-Stake Mining Games with Perfect Randomness

Matheus V.X. Ferreira, S. Matthew Weinberg

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations


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 [4]. 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 [21]. 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 ofProof-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 Proofof- 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.

Original languageEnglish (US)
Title of host publicationEC 2021 - Proceedings of the 22nd ACM Conference on Economics and Computation
PublisherAssociation for Computing Machinery, Inc
Number of pages21
ISBN (Electronic)9781450385541
StatePublished - Jul 18 2021
Event22nd ACM Conference on Economics and Computation, EC 2021 - Virtual, Online, Hungary
Duration: Jul 18 2021Jul 23 2021

Publication series

NameEC 2021 - Proceedings of the 22nd ACM Conference on Economics and Computation


Conference22nd ACM Conference on Economics and Computation, EC 2021
CityVirtual, Online

All Science Journal Classification (ASJC) codes

  • Computational Theory and Mathematics
  • Computer Networks and Communications


  • Nash equilibrium
  • cryptocurrency
  • energy-efficiency
  • proof-of-stake blockchains
  • random beacons


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