In traditional finance, markets are built on order books. Buyers and sellers place orders at specific prices, and a central intermediary matches them. Decentralised Finance (DeFi) replaces this model with something fundamentally different: automated, permissionless liquidity pools.

This structure is managed by an Automated Market Maker (AMM). An AMM is a protocol that uses a mathematical formula to price assets within a pool. It allows digital assets to be traded automatically and without the need for traditional market makers. Anyone can become a liquidity provider (LP) by depositing an equivalent value of two tokens into a pool, receiving LP tokens in return that represent their share. These LP tokens accrue trading fees generated by the pool.

The first generation of widely adopted AMMs, like Uniswap v2, are Constant Product Market Makers (CPMMs). They operate on a simple but powerful principle. The protocol ensures that the product of the quantities of the two tokens in a liquidity pool remains constant, or at least, it should remain constant after a trade is executed, ignoring fees.

When a trader wants to buy token A, they add token B to the pool. To keep $k$ constant, the amount of token A must decrease. The ratio of tokens in the pool determines the price. This design provides liquidity across all possible prices, from zero to infinity. While robust, this is incredibly capital inefficient. Most assets trade within a relatively narrow price range, meaning the vast majority of the liquidity in a CPMM pool is never used.

Uniswap v3 introduced a major innovation: concentrated liquidity. This model allows LPs to allocate their capital to a specific price range of their choosing. Instead of providing liquidity along the entire price curve from zero to infinity, an LP can, for example, provide liquidity for the ETH/USDC pair only within the $2,900 to $3,100 range.

The trade-off is increased risk and management overhead. If the price moves outside an LP's specified range, their position becomes inactive and stops earning fees. Their entire liquidity is converted into the single asset that has fallen in relative value. LPs must actively manage their positions to stay within profitable ranges.

For stablecoins or other assets expected to trade closely, even concentrated liquidity isn't optimal. Protocols like Curve Finance use a different formula, a 'Stableswap invariant'. This curve is much flatter around the target price (e.g., $1.00), allowing for very large trades with minimal price impact, or slippage. It behaves like a constant product formula only when the price deviates significantly from the peg, providing stability.

AMMs don't have access to external market data; they only know the ratio of assets within their pools. So what keeps the price of ETH in a Uniswap pool aligned with its price on Coinbase? Arbitrage.

If the price of ETH in a pool is lower than on external exchanges, arbitrageurs will buy the cheaper ETH from the pool, pushing its price up. They then sell it on the external exchange for a profit. If the price in the pool is higher, they do the reverse. This constant activity, driven by profit, acts as a rebalancing mechanism that keeps AMM prices consistent with the broader market.

Now, let's check your understanding of these core DeFi mechanics.

Understanding these different AMM designs and the role of arbitrage is crucial for evaluating the efficiency, risk, and competitive positioning of any DeFi protocol.