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A Lucas Critique to the Difficulty Adjustment Algorithm of the Bitcoin System

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.

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A Lucas Critique to the Difficulty Adjustment Algorithm of the Bitcoin System

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  1. 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)

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

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

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

  5. Policy Goal • : winning rate • Probability of {hash value < difficulty target} • Proportional to the reciprocal of “difficulty”. • : (global) hash rate • Block time Exponential dist. with intensity . Average block time: . By controlling , we want to satisfy

  6. Current Bitcoin DAA • Periodic adjustment (every 2016 blocks 2 weeks) Averageblock time in previous 2016 blocks = Ideal block time (= 10 minutes) • Too slow Increase the winning rate • Too fast Decrease the winning rate • More justification?

  7. Sample Analogue • Maximum likelihood estimate of the hash rate in previous 2016 blocks: • Bitcoin DAA can be interpreted as • Sample Analogue: Bitcoin DAA achieves the policy goal by using the (estimated) historical hash rate. -1 Averageblock time in previous 2016 blocks =

  8. Miners’ Incentive • Larger winning rate Mining more profitable! • More likely to win the prize. • More miners enter the market. • Turn on/off mining ASIC Small switching cost • Change in winning rate also changes the hash rate. does NOT guarantee

  9. Hash Rate Winning Rate 0

  10. Hash Rate Policy Curve Winning Rate 0

  11. Hash Rate Supply Curve (Hash rate is increasing in winning rate) Policy Curve Winning Rate 0

  12. Hash Rate Supply Curve (Hash rate is increasing in winning rate) Policy Curve Winning Rate 0

  13. Hash Rate Supply Curve (Hash rate is increasing in winning rate) Policy Curve Winning Rate 0

  14. Hash Rate Want to choose to achieve this point! Policy Curve Winning Rate 0

  15. Hash Rate Supply Curve (Hash rate is increasing in winning rate) Policy Curve Winning Rate 0

  16. Hash Rate Supply Curve (Hash rate is increasing in winning rate) Policy Curve Winning Rate 0

  17. Hash Rate Supply Curve (Hash rate is increasing in winning rate) Policy Curve Too slow block generation! Winning Rate 0

  18. Hash Rate Supply Curve (Hash rate is increasing in winning rate) Policy Curve Winning Rate 0

  19. Hash Rate Supply Curve (Hash rate is increasing in winning rate) Policy Curve Winning Rate 0

  20. Hash Rate Supply Curve (Hash rate is increasing in winning rate) Overshoot. Fails to select the ideal winning rate (). Policy Curve Winning Rate 0

  21. Hash Rate Winning Rate 0

  22. Hash Rate Elastic hash supply The winning rate never converges to the policy goal. Winning Rate 0

  23. Simulation • Replicate the situation of late 2018. • Per hash reward attained the historical minimum.

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

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

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

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

  28. Alternative: Bcash DAA • Bitcoin Cash (Bcash) is another blockchain platform. • Hardforked from Bitcoin Share many structures. • Bcash updates the winning rate continually (every period). • Look at the total block time of previous 144 blocks. • If and were constant, this DAA also achieves . • Replace DAA equation Obtain economy under new DAA.

  29. Intuition (Bitcoin DAA) • During the period of observation, an identical winning rate is used. • DAA estimates . Supply Curve Updated Data point Policy Curve 0

  30. Intuition (Bitcoin cash DAA) • is updated every period. • Historical hash rate fluctuates around . • Take average Closer to ! Supply Curve Updated point is closer to the steady state. Data points vary!! Policy Curve 0

  31. Local (In)Stability (Bitcoin DAA) Theorem 1: Under the Bitcoin DAA, iff . Where • If , the winning rate oscillates and diverges.

  32. Local Stability (Bitcoin cash DAA) Theorem 2: Under the Bcash DAA, iff . • Proof: Evaluate eigenvalues of the characteristic equation. • Much weaker than the hypothesis of Theorem 1.

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