An Economic Analysis of Difficulty Adjustment Algorithms in Proof-of-Work Blockchain Systems

54 Pages Posted: 4 Jul 2019

See all articles by Shunya Noda

Shunya Noda

Vancouver School of Economics, University of British Columbia

Kyohei Okumura

Department of Economics, Northwestern University

Yoshinori Hashimoto

BUIDL, Ltd.

Date Written: June 26, 2019

Abstract

The design of the Bitcoin difficulty adjustment algorithm (DAA) is vulnerable as it dismisses miners’ responses to policy changes. We develop an economic model of the Proof-of-Work blockchain system. Our model allows miners to pause operation when it is not profitable. Hence, the supply of aggregate hash power can be elastic in the cryptocurrency price and the difficulty of the mining puzzle. We prove that, when the hash supply is elastic, the Bitcoin DAA fails to stabilize the block arrival rate. In contrast, the DAA of another cryptocurrency, Bitcoin Cash, is stable under a general condition. We also provide empirical evidence and simulation results supporting the model’s prediction. Our results indicate that the current Bitcoin system might collapse once a sharp price reduction lowers the mining reward. While this crisis can be prevented through upgrading, miners may disagree because many of them obtain a larger profit from an unstable DAA.

Keywords: Blockchain, Proof-of-Work, Difficulty Adjustment, Mining, Market Design

JEL Classification: C61, D47, G20, L86

Suggested Citation

Noda, Shunya and Okumura, Kyohei and Hashimoto, Yoshinori, An Economic Analysis of Difficulty Adjustment Algorithms in Proof-of-Work Blockchain Systems (June 26, 2019). Available at SSRN: https://ssrn.com/abstract=3410460 or http://dx.doi.org/10.2139/ssrn.3410460

Shunya Noda (Contact Author)

Vancouver School of Economics, University of British Columbia ( email )

6000 Iona Dr
Vancouver, British Columbia V6T 1L4
Canada

Kyohei Okumura

Department of Economics, Northwestern University ( email )

2211 Campus Dr
Evanston, IL 60208
United States

Yoshinori Hashimoto

BUIDL, Ltd. ( email )

12-10, Sakuragaoka, Shibuya-ku
Neutrino
Tokyo, 150-0031
Japan

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