The Algorithmic Stablecoin Game — Empty Set Døllar
Stablecoins are cryptocurrencies that are designed to track the value of a “stable” asset (eg. 1 USD) or a basket of assets. The high volatility of traditional crypto assets makes them a poor unit of account and store of value, and is one of the main factors limiting their mass adoption. Stablecoins solve this problem, and enable market participants to hold their assets in USD, instead of more volatile cryptocurrencies.
Disclaimer:
- The above reflects the views of the investor and should NOT be construed as investment advice, financial advice or legal advice.
- This information is purely educational and is NOT meant to be taken as a recommendation to buy or sell any product or service. Please do your own research before making any decisions.
- Where relevant, direct quotes & passages have been taken from the sources, whitepapers, and blog posts cited.
Stablecoin adoption has been growing steadily, with total market cap eclipsing the $25 billion mark. USDT is the most dominant stablecoin in use, currently sitting at north of $20 billion in circulating supply, but recently has come under regulatory scrutiny.
High-level, there are three main types of stablecoins:
i) Fiat Collateralized: Each stablecoin is backed 1 for 1 by USD held in bank accounts (eg. USDT, USDC)
ii) Crypto Collateralized: Each stablecoin is backed by over-collateralized crypto assets (eg. DAI, sUSD)
iii) Algorithmic (Seniorage-Style/ Non-Collateralized): Stablecoins where supply can be algorithmically expanded or contracted in order to move the price of the underlying closer to the target price (eg. AMPL, ESD, DSD)
The theoretical underpinnings of algorithmic stablecoins come from Ferdinando Ametrano‘s paper titled “Hayek Money: The Cryptocurrency Price Stability Solution”, Robert Sams’ paper titled “A Note on Cryptocurrency Stabilization: Seigniorage Shares”, and the Basis whitepaper.
In this post we’ll dive into the design and game theoretic aspects of Empty Set Døllar, one of the latest algorithmic stablecoins that has been getting widespread attention recently due to the high APYs being paid out to DAO holders and Uniswap liquidity providers (LPs).
Intro to Empty Set Dollar
Empty Set Døllar (ESD) is an algorithmic stablecoin designed to track the US Dollar. The ESD design leverages coordination between market participants and enforces the peg through two main mechanisms:
i) Expansion: When the price of ESD exceeds $1, the protocol mints new ESD (increasing supply) which are used to purchase debt coupons (explained below) and the remaining are awarded to participants that staked their ESD in the governance DAO, and to Uniswap LPs
ii) Contraction: When the price of ESD falls below $1, the protocol issues debt coupons at a discount, that can be purchased by burning ESD (reducing supply) and can be redeemed at par ($1) during the next expansion
Market Participants & Incentives
High level, ESD market participants can do one of three things:
i) Bond ESD in DAO: Participate in network upside and supply increases
ii) Trade ESD: Speculate on short term price action
iii) Burn ESD for Debt Coupons: Speculate on mean-reversion by purchasing debt coupons during contractions
This is in addition to ESD holders that use it as a stablecoin for regular transactions and/ or supply it into Uniswap pools as LPs.
Contractions
In contractions cycles, when ESD is below $1:
- Demand increases, as traders buy ESD at a discount, speculating on a price reversion back to $1 or acquiring to burn an covert into debt coupons
- Supply decreases, as speculators burn their ESD for debt coupons, that will be redeemable for $1 if the price of ESD reverts back to $1 within a fixed time-frame
This combination of an increase in demand and a decrease in supply puts an upwards pressure on ESD an pushed the price back up to $1 during contractions.
From a game theory perspective, if there is (almost) perfect coordination, all participants would buy the debt coupons, and earn the premium, as the price of ESD would for sure go back above $1.
In reality, you just need a increase in demand an/ or a decrease in supply, to push the price of ESD back up, which will occur if just a portion of market participants have faith that the price go back above $1, and express this view though trading/ buying ESD or burning ESD for debt coupons.
Debt Coupon Market
Source: ESD Whitepaper
To incentivize participants to burn ESD during contractions to purchase debt coupons, the coupon premium was designed to increase with the debt ratio. As the debt ratio increases, the coupon premium also increases, further incentivizing participants to burn their ESD and reduce supply.
The debt ratio R is defined as
The premium curve as a function of R can be represented as
Clearly the premium is zero when the there is no outstanding debt, and increases asymptotically as the outstanding debt amount approaches the total supply.
Given the premium curve, we can now calculate the premium for an order of size n, as a function of the new debt ratio R’.
Once the premium is calculated, we can calculate the coupon amount as follows:
Expansions
In expansion cycles, when ESD is above $1:
- Demand decreases, as traders are less incentivized to buy USD at a premium, and are in-fact incentivized to sell ESD at a premium, speculating on a price reversion back to $1
- Supply increases, as the protocol mints new ESD which are distributed to debt holders followed by networked participants that have staked ESD in the DAO
It’s interesting to note that during expansions, the system offers excellent rewards for network participants not to sell — by bonding their ESD in the DAO, participants are rewarded by the new ESD minted. So there will always be a tradeoff — some participants will sell their ESD while others will bond them in the DAO to maximize rewards.
The amount of ESD minted is designed to increase the supply such that the if the underlying network value doesn’t change, the price of ESD should be $1.
From which we can back-out the required change in supply, to maintain pice stability as follows:
Since supply is also used to payback debt coupons, net supply (supply less debt) is used in the equation above.
Summary
Overall algorithmic stablecoins are a force to be reckoned with. By combining algorithmic game-theory with macro-economics and monetary policy, a new breed of stablecoins are evolving that can track specific underlying assets value in a truly de-centralized, permissionless and capital efficient way.
Will algorithmic stablecoins overcome the initial scaling and network- coordination challenges and be able to maintain price-stability with low volatility? We’re still in the first innings, but so far the initial wave of successful protocol launches and mass community adoption seem very promising indeed!
