Although Bitcoin was intended to be a decentralized digital currency, in practice, mining power is quite concentrated. This fact is a persistent source of concern for the Bitcoin community.
We provide an explanation using a simple model to capture miners' incentives to invest in equipment. In our model, n miners compete for a prize of fixed size. Each miner chooses an investment q_i, incurring cost c_iq_i, and then receives reward q^{\alpha}∑_j q_j^{\alpha}, for some \alpha≥1. When c_i = c+j for all i,j, and α=1, there is a unique equilibrium where all miners invest equally. However, we prove that under seemingly mild deviations from this model, equilibrium outcomes become drastically more centralized. In particular, (a) When costs are asymmetric, if miner i chooses to invest, then miner j has market share at least 1−c_j/c_i. That is, if miner j has costs that are (e.g.) 20% lower than those of miner i, then miner j must control at least 20% of the \emph{total} mining power. (b) In the presence of economies of scale (α>1), every market participant has a market share of at least 1−1/α, implying that the market features at most α/(α−1) miners in total.
We discuss the implications of our results for the future design of cryptocurrencies. In particular, our work further motivates the study of protocols that minimize "orphaned" blocks, proof-of-stake protocols, and incentive compatible protocols.
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Bitcoin: A Natural Oligopoly
We argue that the concentrated production and ownership of Bitcoin mining hardware arise naturally from the economic incentives of Bitcoin mining. We model Bitcoin mining as a two-stage competition; miners compete in prices to sell hardware while competing in quantities for mining rewards. We characterize equilibria in our model and show that small asymmetries in operational costs result in highly concentrated ownership of mining equipment. We further show that production of mining equipment will be dominated by the miner with the most efficient hardware, who will sell hardware to competitors while possibly also using it to mine. This paper was accepted by Kay Giesecke, finance.
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- Award ID(s):
- 1942497
- NSF-PAR ID:
- 10390174
- Date Published:
- Journal Name:
- Management Science
- Volume:
- 68
- Issue:
- 7
- ISSN:
- 0025-1909
- Page Range / eLocation ID:
- 4755 to 4771
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1287/mnsc.2021.4095
