AMM (Automated Market Maker)

In an AMM the price is a deterministic function of the reserve state, known as a bonding curve. The canonical model is the constant product, with the formula x times y equals k, where x and y are the reserves of the two assets in the pair and k is an invariant preserved on each swap before fees. Buying an asset lowers its reserve and raises the other, moving the price along the curve. Variants exist. Uniswap v3 (May 2021) introduced concentrated liquidity within a chosen price range, Curve uses a StableSwap curve optimal for pegged assets, and Balancer generalizes to pools of N assets with arbitrary weights. Key parameters are the reserves, the invariant k, the per-swap fee tier (for example 0.01%, 0.05%, 0.30% or 1% on Uniswap) and, in v3, the price range or ticks.

It solves the problem of always-on liquidity without professional market makers or an order book. Anyone provides liquidity and anyone trades 24/7. It is the foundation that made swap-based DeFi viable. It introduces its own effects, such as slippage and impermanent loss for the liquidity provider, which are worth sizing before committing capital.