An automated market maker, or AMM, is a mechanism for decentralized trading that uses liquidity pools and mathematical formulas instead of a traditional order book where buyers and sellers submit individual orders.

In a typical AMM, a liquidity pool holds reserves of multiple assets. A trader interacts with a smart contract rather than directly matching with a specific counterparty. The contract changes the reserves according to the mathematical model used by the protocol.

One well-known model is based on a constant-product relationship. In simplified form, it can be represented as x * y = k, where x and y represent the reserves of two assets. The exact implementation also accounts for fees and protocol-specific rules.

Because the reserves change after every trade, the execution price depends on the size of the transaction relative to available liquidity. A large transaction can move the pool price substantially and create higher slippage.

Liquidity is supplied by liquidity providers. They deposit assets into the pool and may receive a portion of trading fees. In return, they accept market and smart-contract risks, including impermanent loss.

Different AMM designs use different mathematical curves and liquidity models. Some are optimized for volatile assets, while others are designed for assets whose prices normally remain close to one another, such as certain stablecoins.

An AMM therefore combines a pricing mechanism, a liquidity mechanism, and an incentive system. External arbitrage traders help align pool prices with broader markets, while liquidity providers supply the capital required for continuous trading.