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A Note on the Non-proportionality of Winning Probabilities in Bitcoin

Author

Listed:
  • José Parra-Moyano

    (IMD Lausanne)

  • Gregor Reich

    (Tsumcor Research AG)

  • Karl Schmedders

    (IMD Lausanne)

Abstract

The security of any proof-of-work blockchain protocol is based upon the assumption that the probability of a miner finding the next valid block is proportional to that miner’s hashing power and constant throughout the process of mining that block (i.e., that the mining process is a “memoryless” process). While the literature assumes that the mining process is indeed memoryless, in this paper we use deductive reasoning to show how, given the finiteness of hashing functions’ domains, this is not the case. This implies that the Bitcoin protocol induces a centralization of miners’ hashing power, which in turn threatens the long-term viability of Bitcoin and of other cryptocurrencies based on similar protocols. The novelty of this paper stems from our documenting of a previously unrecognized flaw in the incentive system sustaining Bitcoin’s security.

Suggested Citation

  • José Parra-Moyano & Gregor Reich & Karl Schmedders, 2024. "A Note on the Non-proportionality of Winning Probabilities in Bitcoin," Computational Economics, Springer;Society for Computational Economics, vol. 64(3), pages 1697-1714, September.
    • Handle: RePEc:kap:compec:v:64:y:2024:i:3:d:10.1007_s10614-023-10503-2
    DOI: 10.1007/s10614-023-10503-2
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    References listed on IDEAS

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    1. Luisanna Cocco & Michele Marchesi, 2016. "Modeling and Simulation of the Economics of Mining in the Bitcoin Market," PLOS ONE, Public Library of Science, vol. 11(10), pages 1-31, October.
    2. Lin William Cong & Zhiguo He & Jiasun Li & Wei Jiang, 2021. "Decentralized Mining in Centralized Pools [Concentrating on the fall of the labor share]," The Review of Financial Studies, Society for Financial Studies, vol. 34(3), pages 1191-1235.
    3. Hanna Halaburda & Guillaume Haeringer & Joshua Gans & Neil Gandal, 2022. "The Microeconomics of Cryptocurrencies," Journal of Economic Literature, American Economic Association, vol. 60(3), pages 971-1013, September.
    4. Luisanna Cocco & Michele Marchesi, 2016. "Modeling and Simulation of the Economics of Mining in the Bitcoin Market," Papers 1605.01354, arXiv.org.
    5. Lin William Cong & Ye Li & Neng Wang, 2021. "Tokenomics: Dynamic Adoption and Valuation [The demand of liquid assets with uncertain lumpy expenditures]," The Review of Financial Studies, Society for Financial Studies, vol. 34(3), pages 1105-1155.
    6. Pavel Ciaian & d’Artis Kancs & Miroslava Rajcaniova, 2021. "The economic dependency of bitcoin security," Applied Economics, Taylor & Francis Journals, vol. 53(49), pages 5738-5755, October.
    7. Benigno, Pierpaolo & Schilling, Linda M. & Uhlig, Harald, 2022. "Cryptocurrencies, currency competition, and the impossible trinity," Journal of International Economics, Elsevier, vol. 136(C).
    8. Easley, David & O'Hara, Maureen & Basu, Soumya, 2019. "From mining to markets: The evolution of bitcoin transaction fees," Journal of Financial Economics, Elsevier, vol. 134(1), pages 91-109.
    9. Chiu, Jonathan & Koeppl, Thorsten, 2017. "The Economics of Cryptocurrencies - Bitcoin and Beyond," Queen's Economics Department Working Papers 274715, Queen's University - Department of Economics.
    10. Rainer Böhme & Nicolas Christin & Benjamin Edelman & Tyler Moore, 2015. "Bitcoin: Economics, Technology, and Governance," Journal of Economic Perspectives, American Economic Association, vol. 29(2), pages 213-238, Spring.
    11. Adam S. Hayes, 2019. "Bitcoin price and its marginal cost of production: support for a fundamental value," Applied Economics Letters, Taylor & Francis Journals, vol. 26(7), pages 554-560, April.
    12. Can, Burak & Leth Hougaard, Jens & Pourpouneh, Mohsen, 2022. "On reward sharing in blockchain mining pools," Games and Economic Behavior, Elsevier, vol. 136(C), pages 274-298.
    13. Jacob D. Leshno & Philipp Strack, 2020. "Bitcoin: An Axiomatic Approach and an Impossibility Theorem," American Economic Review: Insights, American Economic Association, vol. 2(3), pages 269-286, September.
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