Attacks on Dynamic DeFi Interest Rate Curves

As decentralized money market protocols continue to grow in value locked, there have been a number of optimizations proposed for improving capital efficiency. One set of proposals from Euler Finance and Mars Protocol is to have an interest rate curve that is a proportional-integral-derivative (PID) controller. In this paper, we demonstrate attacks on proportional and proportional-integral controlled interest rate curves. The attack allows one to manipulate the interest rate curve to take a higher proportion of the earned yield than their pro-rata share of the lending pool. We conclude with an argument that PID interest rate curves can actually \emph{reduce} capital efficiency (due to attack mitigations) unless supply and demand elasticity to rate changes are sufficiently high.