Rational Ponzi Games in Algorithmic Stablecoin

TL;DR

This paper investigates whether algorithmic stablecoins function as rational Ponzi games, providing a model to analyze their stability and applying it to real-world projects like Ampleforth and TerraUSD.

Contribution

It introduces a rational Ponzi game model for algorithmic stablecoins and applies it to analyze their stability and market behavior.

Findings

The model clarifies conditions under which stablecoins can be rational Ponzi games.

Analysis of Ampleforth and TerraUSD demonstrates the model's applicability.

Insights into the stability and collapse mechanisms of algorithmic stablecoins.

Abstract

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.