Rational Ponzi Games in Algorithmic Stablecoin

Algorithmic stablecoins (AS) are one special type of stablecoins that are not backed by any asset (equiv. without collateral). They stand to revolutionize the way a sovereign fiat operates. As implemented, these coins are poorly stabilized in most cases, easily deviating from the price target or even falling into a catastrophic collapse (a.k.a. Death spiral), and are as a result dismissed as a Ponzi scheme. However, is this the whole picture? In this paper, we try to reveal the truth and clarify such a deceptive concept. We find that Ponzi is basically a financial protocol that pays existing investors with funds collected from new ones. Running a Ponzi, however, does not necessarily imply that any participant is in any sense losing out, as long as the game can be perpetually rolled over. Economists call such realization as a $\mathit{\text{rational}}\mathit{\text{Ponzi}}\mathit{\text{game}}$. We thereby propose a rational model in the context of AS and draw its holding conditions. We apply the model to examine: $\mathit{\text{whether}}\mathit{\text{or}}\mathit{\text{not}}\mathit{\text{the}}\mathit{\text{algorithmic}}\mathit{\text{stablecoin}}\mathit{\text{is}}\mathit{\text{a}}\mathit{\text{rational}}\mathit{\text{Ponzi}}\mathit{\text{game.}}$ Accordingly, we discuss two types of algorithmic stablecoins ($\text{Rebase}$ & $\text{Seigniorage shares}$) and dig into the historical market performance of two impactful projects ($\text{Ampleforth}$ & $\text{TerraUSD}$, respectively) to demonstrate the effectiveness of our model.