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 \textit{rational Ponzi game}. We thereby propose a rational model in the context of AS and draw its holding conditions. We apply the model to examine: \textit{whether or not the algorithmic stablecoin is a rational Ponzi 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.

翻译：算法稳定币（AS）是一种不以任何资产（即无抵押）为支撑的特殊稳定币，有望彻底改变主权法币的运作方式。在实际应用中，这些代币在多数情况下稳定性较差，容易偏离目标价格甚至陷入灾难性崩盘（即“死亡螺旋”），因此常被斥为庞氏骗局。然而，事实果真如此吗？本文试图揭示真相并厘清这一具有迷惑性的概念。我们发现，庞氏本质上是一种利用新投资者资金向现有投资者支付回报的金融协议。但只要游戏能够无限期持续下去，运行庞氏结构未必意味着任何参与者会遭受损失——经济学家将这种认知称为“理性庞氏博弈”。为此，我们在算法稳定币语境下提出一个理性模型，并推导其存续条件。应用该模型检验“算法稳定币是否为理性庞氏博弈”这一命题，我们继而讨论了两类算法稳定币（Rebase型与Seigniorage Shares型），并深入分析两个具有影响力的项目（Ampleforth与TerraUSD）的历史市场表现，以验证模型的有效性。