Automated Market Maker (AMM) With Constant Product Formula

The most common AMM model uses the constant product formula, which ensures that the product of the reserves of two assets remains constant during trades.

For $AAA, this can be expressed as:

x y = k

Where:

• x: Reserve of $AAA tokens in the liquidity pool.

• y: Reserve of the paired asset (e.g., stablecoins like USDC or ETH).

• k: A constant representing the invariant product.

When a user swaps $AAA for the paired asset, the new reserves are calculated as:

x' = x - x, y' = y + y

With the condition,

x' y' = k

This ensures that the price of $AAA adjusts dynamically based on trade volume, incentivizing arbitrageurs to correct imbalances.