Paper 2018/780

A Game Theoretic Analysis of Resource Mining in Blockchain

Rajani Singh, Ashutosh Dhar Dwivedi, Gautam Srivastava, Agnieszka Wiszniewska-Matyszkiel, and Xiaochun Cheng


Blockchain and cryptocurrency are a hot topic in today’s digital world. In this paper, we create a game theoretic model in continuous time. We consider a dynamic game model of the bitcoin market, where miners or players use mining systems to mine bitcoin by investing electricity into the mining system. Although this work is motivated by BTC, the work presented can be applicable to other mining systems similar to BTC. We propose three concepts of dynamic game theoretic solutions to the model: Social optimum, Nash equilibrium and myopic Nash equilibrium. Using the model that a player represents a single “miner” or a “mining pool”, we develop novel and interesting results for the cryptocurrency world.

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Preprint. MINOR revision.
BlockchainBitcoin MiningDynamic Game TheoryDifferential GameHamilton-Jacobi-Bellman EquationSocial OptimumNash Equilibriummyopic Nash equilibriumPigovian Tax
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ashudhar7 @ gmail com
2019-11-24: last of 3 revisions
2018-09-01: received
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      author = {Rajani Singh and Ashutosh Dhar Dwivedi and Gautam Srivastava and Agnieszka Wiszniewska-Matyszkiel and Xiaochun Cheng},
      title = {A Game Theoretic Analysis of Resource Mining in Blockchain},
      howpublished = {Cryptology ePrint Archive, Paper 2018/780},
      year = {2018},
      note = {\url{}},
      url = {}
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