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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Ignore the Extra Zeroes: Variance-Optimal Mining Pools
Mining pools decrease the variance in the income of cryptocurrency miners (compared to solo mining) by distributing rewards to participating miners according to the shares submitted over a period of time. The most common definition of a “share” is a proof-of-work for a difficulty level lower than that required for block authorization—for example, a hash with at least 65 leading zeroes (in binary) rather than at least 75.
The first contribution of this paper is to investigate more sophisticated approaches to pool reward distribution that use multiple classes of shares—for example, corresponding to differing numbers of leading zeroes—and assign different rewards to shares from different classes. What’s the best way to use such finer-grained information, and how much can it help? We prove that the answer is not at all: using the additional information can only increase the variance in rewards experienced by every miner.
Our second contribution is to identify variance-optimal reward-sharing schemes. Here, we first prove that pay-per-share rewards simultaneously minimize the variance of all miners over all reward-sharing schemes with long-run rewards proportional to miners’ hash rates. We then show that, if we impose natural restrictions including a no-deficit condition on reward-sharing schemes, then the pay-per-last-N-shares method is optimal.
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- Award ID(s):
- 2006737
- NSF-PAR ID:
- 10310909
- Date Published:
- Journal Name:
- International Conference on Financial Cryptography and Data Security
- 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
- Conference Paper:
- https://doi.org/10.1007/978-3-662-64331
