Explain the Difference between an Order Book Model and a Constant Product Formula Model for Liquidity

The order book model relies on a centralized list of limit buy and sell orders placed by individual traders. The price is determined by matching these bids and asks.

The constant product formula model, typical of AMMs, uses an algorithmic approach where the product of the quantities of two tokens in a pool remains constant (x y = k). Price changes are determined by the size of the trade relative to the pool's reserves, not by matching individual orders.