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

49 Pages Posted: 4 Jul 2019 Last revised: 15 Mar 2022

See all articles by Shunya Noda

Shunya Noda

University of Tokyo - Faculty of Economics; 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

We develop an economic model of the Proof-of-Work blockchain system. We demonstrate that, when the hash supply is highly elastic, the Bitcoin difficulty adjustment algorithm (DAA) fails to stabilize the block arrival rate. In contrast, the DAA of another cryptocurrency, Bitcoin Cash, is stable under a weak condition. We also provide empirical evidence and simulation results supporting the model’s prediction. 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 a large fraction of miners profit from the instability of DAAs.

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)

University of Tokyo - Faculty of Economics ( email )

7-3-1 Hongo, Bunkyo-ku
Tokyo, 113-0033
Japan

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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