Searching for Optimal Strategies in Proof-of-Stake Mining Games with Access to External Randomness

This webpage presents all materials related to my thesis submitted in partial fulfillment of the requirements for the degree of Bachelor of Science in Engineering in the Department of Computer Science at Princeton University. This thesis was advised by Prof. Matt Weinberg and Dr. Matheus Ferreira

The most up-to-date materials are linked below:

Report Presentation Computations Source Files Figures GitHub Code Code Results

Although I have tried to be as comprehensive as possible, the subject matter of this thesis may be confusing to those who do not have a background in cryptocurrency or game theory. Below, I have listed some publicly available resources which should provide a working knowledge of these topics:

• Bitcoin and Cryptocurrency Technologies (Chapter 1) by Arvind Narayanan, Joseph Bonneau, Edward Felten, Andrew Miller, Steven Goldfeder
• An Introduction to Game Theory (Chapter 2) by Martin J. Osborne

Then, the most closely related academic papers to this thesis are:

• Majority is not Enough: Bitcoin Mining is Vulnerable by Ittay Eyal and Emin Gün Sirer
• Proof-of-Stake Mining Games with Perfect Randomness by Matheus V. X. Ferreira and S. Matthew Weinberg

I am more than happy to recommend alternative resources upon request.

Please use this link to reach out to the author with any question, comments, or concerns. Or, send an email to any of the following addresses:

• anthonynhein@gmail.com
• anhein@princeton.edu

Check out my personal website www.anthonyhein.com to learn more about me.

In light of the massive energy consumption due to proof-of-work cryptocurrency mining protocols, more environmentally-friendly proof-of-stake mining protocols are becoming increasingly desirable. However, to sustain a healthy mining ecosystem, a mining protocol must be fairly robust against strategic manipulation. This paper continues work by Ferreira and Weinberg (link) to determine the feasibility of strategic manipulation under a proof-of-stake mining protocol with access to external randomness. Previously, Ferreira and Weinberg showed that strategic manipulation is always possible when some miner owns more than 32.47% of the stake but never possible when every miner owns less than 30.80% of the stake. Here, we are able to improve both bounds in showing that strategic manipulation is always possible when some miner owns more than 32.35% of the stake but never possible when every miner owns less than 31.89% of the stake.

In conducting this research, I am not recommending for or against investment in cryptocurrency. Anyone who considers investing in cryptocurrency should be well-educated on the subject and understand the risks involved.