I'm not a fan of Cardano, however I tried to study the functioning of its algorithmic stable Djed.
Even if little used, there are 3 stablecoin on Cardano, 2 of which are active. Ausd is an overcollateralized algorithmic stablecoin, Usda is collateralized 1:1 by real dollars (such as Usdt and Usdc) and Djed which is partially algorithmic but overcollateralized by Ada and uses the Shen token as a reserve coin. Djed was developed by Cardano developers and Coti Group (Coti is a payment solution, similar to Iota).

HOW DJED WORKS: OVERCOLLATERALIZED ALGORITHMIC STABLE
Djed is an Egyptian word and means "stability" and in the future we will see if it will really be like this but how does it work?
When Djed's price is too high (over $1), the contract will automatically issue more tokens. When the price falls, the contract will buy more Djed to help raise the price, all while also managing a token reserve that allows the value to be kept constant.
Djed's overcollateralization is 400%, i.e. every $4 of Ada is minted $1 of Djed. The stable would find itself under-collateralized with the peg in dangerous, if Ada suffered a loss of more than 75% in a short time. If the mint ratio was 1:1 providing $1 of Ada I would get $1 of Djed so when Ada goes down there wouldn't be enough Djed to pay off all the redeem.
The Shen token is used in the incentive ecosystem which should absorb the volatility of Ada and help maintain the peg.
1 Shen is worth a little more than 1 Ada and increases as the price of Ada increases (and vice versa) in a similar %. Shen price is given by the ratio between equity and the number of Shen in circulation:

Basically Shen is collateralized by Ada.
If I provide Ada as liquidity in the Djed smart contract, you receive Shen. Shen is the incentive to make the system over-collateralized. The mechanism works via mint/burn: I deposit Ada and I mint Djed, receiving the Shen. I redeem Ada and burn Djed.

Below 400% collateralization, Djed's mint is blocked but I can still mint Shen (and not burn them). This should avoid manipulation of Djed's peg.
Over 800% I can no longer mint Shen but only burn them. If too many Shen (over 800%) are minted, the incentives would be too small for the liquidity provider and the system could become unstable.
If the price of Ada increases, the % collateralization increases therefore the risk factor decreases (even without adding more collateral). If, on the other hand, the price of Ada falls, the collateralization % also decreases and you cannot burn the Shen and mint new Djed (I can burn the Djed by redeeming the Ada or increase them by increasing the collateralization).

INCENTIVES
Different incentives are used for Djed to keep the peg:
1) Each mint/burn operation (by Djed and Shen) increases the "request fees" (reserve pool) which are distributed among those who provide liquidity in Ada and therefore to Shen holders.

2) Another incentive is the reserve of the Ada themselves which are staked, generating an income

3) Shens could generate additional income if provided as liquidity in a pool on an AMM

4) Shen himself, having a tradable asset, could provide an additional incentive due to its market fluctuations

If you want to "play" by simulating Djed's mint/burn you can use this tool: PlayWithDjed

My thoughts? I have not formed a precise opinion on this system which takes ideas from other protocols and puts them together. There are references to Ust (obviously), to Dai (overcollateralisation), to Anchor Protocol (Anchor staked the borrowers' collateral and a part of this percentage was transferred to the lenders. Anchor was a lending platform, however conceptually the incentive to staking collateral comes from there) and Tomb Finance (Tomb token was pegged to FTM via Tbond and Tshare, where the user was incentivized to sell, buy or stake depending on the Tomb price. Again, the smart contract had thresholds in which it blocked the possibility of minting and burning tokens. Clearly we are talking about a quite different system but broadly speaking, some ideas also come from here).
I think the real "stress test" for Djed will be adoption. If this stable reaches a market cap close to one billion, it will only be there that the going will get tough.

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