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

This repository contains the codes and notebooks used for the following paper:

An Economic Analysis of Difficulty Adjustment Algorithms in Proof-of-Work Blockchain Systems
Shunya Noda (University of British Columbia), Kyohei Okumura (Northwestern Univerisity), Yoshinori Hashimoto (Turingum K.K.,)
https://ssrn.com/abstract=3410460

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.

Resources

• Notebook for impulse response

  • Section 4.4

• Notebook for empirical analysis

  • Section 5

• Notebook for simulation

  • Section 6.1, 6.2, 6.3

• Notebook for simulation about miners' profit

  • Section 6.5

• Notebook for ASERT

  • Section 7

• Notebook for Robustness Check 1: Transaction fee adjustment

  • Section 8.1

• Notebook for Robustness Check 2: Price adjustment

  • Section 8.2