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How Does a ‘Liquidity Pool’ in DeFi Differ from a Centralized Exchange Order Book?

A liquidity pool, used by Automated Market Makers (AMMs) on DEXs, holds two or more tokens and uses a mathematical formula to determine the price. It does not use a traditional order book of bids and asks.

Trades are executed against the pool's assets. The CEX order book uses matching engine logic to pair buyers and sellers.

Liquidity pools introduce 'impermanent loss' but eliminate the need for a direct counterparty.

How Would This Formula Change for a Liquidity Pool Governed by a Constant Mean or Constant Sum Formula?
What Is an Automated Market Maker (AMM) and How Does It Differ from a Traditional Order Book?
How Does the ‘Fee Structure’ Differ between a Centralized Exchange (CEX) and a Decentralized Exchange (DEX) AMM?
How Does a Decentralized Exchange (DEX) Differ from a Centralized Exchange (CEX) in Terms of Liquidity Provision?