Improving DeFi Mechanisms with Dynamic Games and Optimal Control: A Case Study in Stablecoins

TL;DR

This paper shows that it can mitigate adverse depeg events that inevitably arise in a fixed-redemption scheme such as MakerDao's DAI and generally outperform a simpler, adaptive-redemption scheme such as RAI in the task of targeting a desired market price.

Abstract

Stablecoins are a class of cryptocurrencies which aim at providing consistency and predictability, typically by pegging the token's value to that of a real world asset. Designing resilient decentralized stablecoins is a challenge, and prominent stablecoins today either (i) give up on decentralization, or (ii) rely on user-owned cryptocurrencies as collateral, exposing the token to exogenous price fluctuations. In this latter category, it is increasingly common to employ algorithmic mechanisms to automate risk management, helping maintain the peg. One example of this is Reflexer's RAI, which adapts its system-internal exchange rate (redemption price) to secondary market conditions according to a proportional control law. In this paper, we take this idea of active management a step further, and introduce a new kind of control scheme based on a Stackelberg game model between the token protocol and its users. By doing so, we show that (i) we can mitigate adverse depeg events that inevitably arise in a fixed-redemption scheme such as MakerDao's DAI and (ii) generally outperform a simpler, adaptive-redemption scheme such as RAI in the task of targeting a desired market price. We demonstrate these results through extensive simulations over a range of market conditions.

Figures (5)

• Figure 1: Arbitrage Makes the Difference: In the absence of arbitrage ($K_A=0$), RAI and DAI both struggle to regain their peg. When $K_A=50$ we see the arbitrageur actions correlate across all three tokens; however, only UTAI's redemption price decisions motivates unique speculator agent behavior which helps the system to regain the peg smoothly and within a shorter duration. In particular, note the trends highlighted within the red windows. UTAI regains the peg with or without arbitrage.
• Figure 2: A sample path from each scenario in \ref{['section:scenarios']}.
• Figure 3: Four sample runs exemplifying our four different scenarios selected from the "no arbitrage" ($K_A = 0$) case. Each panel highlights unique behavior of UTAI under each condition. Specifically, the light orange series ($\alpha^{UTAI}$) are the controlled redemption prices which help guide the dark orange $p^{Stb}$ to the peg of $1. Unlike RAI, which had to be re-tuned for the best results in each case/scenario, UTAI is naturally able to adapt to the scenario due to inherent reasoning through the predictive bilevel game model. In the absence of arbitrageurs, DAI's market price depegs and essentially tracks the exogenous demand.
• Figure 4: (Left) The demand shock triggered by token burning pressure leads to a deleveraging spiral in the price of DAI. RAI adapts but proportional control is slow to recover the peg. UTAI is quickest to recover. (Right) System collateral levels overlaid with a crashing ETH price pattern. The dashed red line depicts the threshold at which mass burning is activated in simulation; the bold red line shows the absolute minimum collateralization ratio. DAI performs worst, as any arbitraging is drowned out by the speculator's mass burn actions, and the system even falls below the minimum $\beta$ requirement. Both RAI and UTAI mitigate deleveraging by adapting the redemption price, which effectively relaxes the vault constraint temporarily. UTAI stays furthest from the minimum collateralization threshold during the shock.
• Figure 5: Results from \ref{['tbl:mc_stats']} pooled and plotted over the 100 time steps. Shading represents a 90% confidence interval over the p-MAD metric.