by Xiaowu Dai (UC Berkeley)

A blockchain-based payment system uses a decentralized network of computers (miners) to verify transactions and maintain the ledger containing transaction history. The blockchain design is governed by a computer protocol and does not require trust in any centralized organization. The system supports only transactions of its native coins, such as bitcoins, which have value because payment recipients have confidence in their future usefulness. The design of such a novel system was proposed by [11]. It is of interest to study the mechanism design of the blockchain payment system and related questions on transparency and fairness [1, 6, 7, 13].

This project is connected with what was explored during the Simons Institute’s Fall 2019 program on Proofs, Consensus, and Decentralizing Society, especially with the algorithms and economics questions that emerged from the blockchain-based systems.

The blockchain payment system can be modeled as a two-sided market that intermediates between users and miners [5, 9]. The rise in Bitcoin transaction volume, coupled with limited capacity on the number of blocks that can be posted to the blockchain, raises transaction delays and motivates users to pay transaction fees for service priority. We want to understand how the transaction fees influence users’ willingness to participate in the payment system. Our analysis suggests a simple modification on the design by adding a statistical learning-aid recommendation of transaction fees for users. In particular, we build confidence bands for the regression function \(f(\cdot)\) in the model

\[\text{delay}\ \text{ti}\text{me} = f\left( \text{transaction}\ \text{fee} \right) + g\left( \text{control} \right) + \text{disturbance}\text{.}\]

Here, the control variable includes the number of pending transactions, fees of pending transactions, current infrastructure level, rate of block addition to the ledger, and history of random arrival of transactions, among others [12]. The \(f(\cdot)\) is the main nonparametric regression function that we want to infer, and the function \(g(\cdot)\) is the nuisance parameter. The dimension of the control vector can be large relative to the sample size. We develop a simple procedure to construct an honest confidence band for \(f(\cdot)\), a method that builds on the recently developed framework (e.g., [2, 3]). The confidence band would cover the true \(f(\cdot)\) at the nominal level (say, 95% level) uniformly over a large function space given a large sample of data. The notion of honesty is closely related to the use of the worst-case criterion that is necessary for good finite-sample performance [10].

This statistical learning-aid recommendation could provide the relationship between the transaction fees and the predicted transaction delay time, together with confidence bands. It leads to several implications. First, the recommendation enables the transparency of the blockchain payment system mechanism. It allows a direct comparison with the traditional payment system operated by a centralized firm like Visa or PayPal. The firm can reverse transactions in case of error or fraud, a property that is lacking in the blockchain payment system. On the other hand, users benefit from the transparency since they can decide which payment system is better for processing the transaction and how to balance the trade-off between transaction fees and transaction delay. Second, the blockchain payment system enjoys the Vickrey, Clarke, Groves (VCG) property in that each user pays a transaction fee equal to the externality on other users caused by delaying others’ transactions [4, 8, 9, 14]. The recommendation also adds the fairness guarantee; that way, with high probability, the transaction fee is close to the actual value of service priority and users avoid paying extra.

**References**

[1] Barber, S., Boyen, X., Shi, E., and Uzun, E. (2012). “Bitter to Better—How to Make Bitcoin a Better Currency.” *International Conference on Financial Cryptography and Data Security*, 399–414. Springer.

[2] Chernozhukov, V., Chetverikov, D., and Kato, K. (2014a). “Anti-Concentration and Honest, Adaptive Confidence Bands.” *Annals of Statistics*, 42(5):1787–1818.

[3] Chernozhukov, V., Chetverikov, D., and Kato, K. (2014b). “Gaussian Approximation of Suprema of Empirical Processes.” *Annals of Statistics*, 42(4):1564–1597.

[4] Clarke, E. H. (1971). “Multipart Pricing of Public Goods.” *Public Choice*, 11(1):17–33.

[5] Easley, D., O’Hara, M., and Basu, S. (2019). “From Mining to Markets: The Evolution of Bitcoin Transaction Fees.” *Journal of Financial Economics*, 134(1):91–109.

[6] Eyal, I., Gencer, A. E., Sirer, E. G., and Van Renesse, R. (2016). “Bitcoin-ng: A Scalable Blockchain Protocol.” *13th USENIX Symposium on Networked Systems Design and Implementation (NSDI 16)*, 45–59.

[7] Eyal, I. and Sirer, E. G. (2014). “Majority is Not Enough: Bitcoin Mining is Vulnerable.” *International Conference on Financial Cryptography and Data Security*, 436–454. Springer.

[8] Groves, T. (1973). “Incentives in Teams.” *Econometrica*, 41(4):617–631.

[9] Huberman, G., Leshno, J. D., and Moallemi, C. (2019). “An Economic Analysis of the Bitcoin Payment System.” Columbia Business School Research Paper.

[10] Li, K.-C. (1989). “Honest Confidence Regions for Nonparametric Regression.” *Annals of Statistics*, 17(3):1001–1008.

[11] Nakamoto, S. (2008). “Bitcoin: A Peer-to-Peer Electronic Cash System.” White paper. http://bitcoin.org/bitcoin.

[12] Narayanan, A., Bonneau, J., Felten, E., Miller, A., and Goldfeder, S. (2016). *Bitcoin and Cryptocurrency Technologies: A Comprehensive Introduction*. Princeton University Press.

[13] Sapirshtein, A., Sompolinsky, Y., and Zohar, A. (2016). “Optimal Selfish Mining Strategies in Bitcoin.” *International Conference on Financial Cryptography and Data Security*, 515–532. Springer.

[14] Vickrey, W. (1961). “Counterspeculation, Auctions, and Competitive Sealed Tenders.” *The Journal of Finance*, 16(1):8–37.