CFMM
Also: Constant-Function Market Maker · AMM
An exchange that holds reserves of two or more assets and quotes prices from a formula over those reserves, rather than from an order book.
A constant-function market maker keeps a mathematical relationship between its reserves invariant across every trade. Anyone can trade against it at the price that relationship implies, and the price moves as the reserves change. No counterparty has to be found, because the pool is always the counterparty.
When a pool is at rest
Recent work characterises equilibrium precisely: in a closed two-asset, two-trader setting, an interior state is a unilateral no-trade equilibrium exactly when the pool's marginal price equals both traders' marginal rates of substitution. Not approximately, and not for one of them.
The same work finds that individually rational equilibria are Pareto optimal, and gives conditions determining whether trading first helps or hurts — a question desks usually answer by folklore.
The caveat worth keeping
Closed models describe a world with no external market to arbitrage against. That is a long way from a live pool watched by bots every block. What a closed model buys is a statement exactly true about a simple world, which is firmer ground than a statement approximately true about a complicated one.