A Lucas Critique to the Difficulty Adjustment Algorithm

A Lucas Critique to the Difficulty Adjustment Algorithm of the Bitcoin System @Scaling Bitcoin September 2019 Yoshinori Hashimoto (BUIDL, Ltd. ) Shunya Noda (University of British Columbia) Kyohei Okumura (The University of Tokyo)

BUIDL as a blockchain service provider Consulting & Development Research & Development

Shunya Noda UBC Econ Kyohei Okumura Yoshinori Hashimoto U Tokyo Econ BUIDL, Ltd. (Ph. D. Student) (Researcher)

Design Issue of the Bitcoin System p The Bitcoin community agreed to aim at generating blocks every 10 minutes(on average). n Need to adjust the “difficulty target”. n Difficulty Adjustment Algorithm (DAA) n How should we design it?

Policy Goal p

Current Bitcoin DAA p = Average block time in previous 2016 blocks

Sample Analogue p = Average block time in previous 2016 blocks -1

Miners’ Incentive p

0

0

Supply Curve (Hash rate is increasing in winning rate) 0

Supply Curve (Hash rate is increasing in winning rate) 0

Supply Curve (Hash rate is increasing in winning rate) 0

0

Supply Curve (Hash rate is increasing in winning rate) 0

Supply Curve (Hash rate is increasing in winning rate) 0

Supply Curve (Hash rate is increasing in winning rate) Too slow block generation! 0

Supply Curve (Hash rate is increasing in winning rate) 0

Supply Curve (Hash rate is increasing in winning rate) 0

Supply Curve (Hash rate is increasing in winning rate) 0

0

0

Simulation p Replicate the situation of late 2018. n Per hash reward attained the historical minimum.

Blue line: Ideal Red line: Under Bitcoin DAA p Bitcoin DAA fails to “trace” the ideal outcome. p Block time is highly unstable. We were about to face a crisis in November 2018!

In contrast, the DAA of Bitcoin Cash is shown to be very robust. (See the paper)

Policy Suggestion: (1) We must upgrade Bitcoin DAA. (2) The current DAA of the. Bitcoin Cash system is a good candidate for it.

Thank you! p Original paper download link: p https: //ssrn. com/abstract=3410460

Alternative: Bcash DAA p

Intuition (Bitcoin DAA) Updated p Data point 0

Intuition (Bitcoin cash DAA) Updated point is closer to the steady state. p Data points vary!! 0

Local (In)Stability (Bitcoin DAA) p

Local Stability (Bitcoin cash DAA) p