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.
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