Automated Market Makers (AMM)

How algorithmic protocols replaced the order book with a mathematical formula, why liquidity pools became the foundation of decentralized exchanges, and what a tokenomist needs to know when designing liquidity.

What Is an AMM

AMM (Automated Market Maker) is an algorithmic protocol that replaces the traditional order book with a mathematical formula for swapping tokens. Instead of matching buyers and sellers, an AMM uses liquidity pools and deterministic equations to calculate the price of every trade.

On a centralized exchange, price is determined by matching orders: someone places a limit buy, someone else a limit sell, and the exchange engine matches them. This model requires sufficient order depth and constant presence of market makers. An AMM eliminates this dependency: anyone can swap one token for another at any time, as long as there’s liquidity in the pool.

The first AMM appeared in 2017 (Bancor pioneered the continuous token model), followed by Uniswap V1 in November 2018. The real boom came in 2020–2021 — the so-called DeFi Summer. By 2026, the combined TVL of AMM-based decentralized exchanges exceeds $10 billion, and the model has become the standard for on-chain token trading.

How a Liquidity Pool Works

The AMM mechanism breaks down into four steps:

1. A liquidity provider (LP) deposits tokens. They add a pair of tokens in a specific ratio — for example, ETH and USDC. In return, they receive an LP token confirming their share of the pool.
2. The pool holds reserves of both tokens. A smart contract on the blockchain contains the balances of two (or more) tokens. These reserves are the liquidity available to traders.
3. Price is determined by a formula. With every swap, the protocol recalculates the token ratio in the pool using a mathematical equation. The more of one token is removed from the pool, the more expensive the next unit becomes.
4. A trader performs a swap. They send one token into the pool and receive another. The amount received is calculated by the formula based on current reserves. Each swap incurs a fee (typically 0.3%), which is distributed among LPs.

The Role of LP Tokens

An LP token is a proof of share in the pool. When an LP wants to withdraw their funds, they return (burn) the LP token and receive a proportional share of both tokens from the pool. Important: the token ratio at withdrawal may differ from the ratio at deposit — this is exactly what causes impermanent loss.

Fees and LP Revenue

Every swap generates a fee (trading fee). The standard is 0.3% of the trade amount in Uniswap V2, though V3 offers tiers of 0.01%, 0.05%, 0.3%, and 1%. Fees are automatically added to pool reserves, increasing the value of LP tokens. LP profitability depends on trading volume: the more swaps pass through the pool, the more fees liquidity providers earn.

Pricing Formulas

Constant Product (x * y = k)

The most common AMM formula, used in Uniswap V2, SushiSwap, and PancakeSwap. The product of the two token reserves remains constant after every trade (excluding fees).

The price of token A in units of token B is determined by the ratio of reserves:

The hyperbola x*y=k provides infinite liquidity in both directions: the price approaches infinity as one reserve approaches zero, but never reaches it. The tradeoff — large trades relative to pool size produce significant slippage.

Constant Sum (x + y = k) and StableSwap

The formula x+y=k enables 1:1 swaps with zero slippage, but the pool can be completely drained. For stablecoins (USDC/USDT, DAI/USDC), a curve is needed that behaves like x+y=k for small deviations and like x*y=k for large ones.

Curve Finance solved this with the StableSwap invariant:

The parameter A (amplification coefficient) determines how “flat” the curve is near equilibrium. At A=0, the formula degenerates into constant product; as A approaches infinity, it becomes constant sum. Typical values for stablecoin pools: A = 100–2000.

Concentrated Liquidity

Uniswap V3 introduced concentrated liquidity: an LP places liquidity not across the entire price range from 0 to infinity, but only within a chosen interval [P_a, P_b]. This dramatically increases capital efficiency.

If an LP limits the range to +/-5% of the current price, their capital efficiency increases roughly 20x compared to Uniswap V2. However, if the price moves outside the range, the position stops generating fees and fully converts into one of the tokens.

AMM Types

Weighted Pools (Balancer)

Unlike Uniswap, where both tokens have 50/50 weight, Balancer allows arbitrary weights. The generalized invariant formula:

An 80/20 pool (e.g., 80% project token and 20% ETH) requires the LP to deposit less ETH, lowering the entry barrier and reducing impermanent loss for the project token. This approach is widely used when launching new tokens via Liquidity Bootstrapping Pools (LBP).

Impermanent Loss

Impermanent loss (IL) is the difference between the value of an LP’s assets in the pool and the value of the same assets if they had simply held them without providing liquidity. The loss is called “impermanent” because it disappears if the price returns to the original ratio.

Where the Loss Comes From

When the price of one token rises relative to the other, arbitrageurs equalize the pool price with the market price, taking the underpriced asset and adding the overpriced one. As a result, the LP ends up with more of the depreciated token and less of the appreciated one — worse than simply holding both assets.

The Impermanent Loss Formula

For the constant product model (x*y=k, Uniswap V2):

Reference points:

r is the ratio of the new token price to the initial price. r=2 means the price doubled; r=0.5 means it halved.

When Fees Offset Impermanent Loss

An LP earns fees from every swap. If the annualized fee yield exceeds impermanent loss over the same period, the liquidity provider profits. This requires:

• High trading volume relative to pool size (high capital turnover)
• Moderate volatility of the token pair (IL grows with volatility)
• Additional incentives via governance token rewards (liquidity mining)

AMM Protocol Tokenomics

AMM protocols are themselves tokenomic systems. Here’s how they generate revenue and distribute value.

Revenue Streams

The primary revenue source is trading fees. Every swap generates a fee distributed among participants:

Fee distribution (typical model):

Trader pays fee (0.3%)
  ├── 0.25% → Liquidity providers (LP)
  └── 0.05% → Protocol treasury / token holders

Additional revenue sources:
  ├── Flash loan fees
  ├── Pool creation fees
  └── Protocol-Owned MEV revenue

Governance Token and Incentives

Most AMM protocols issue a governance token: UNI for Uniswap, CRV for Curve, BAL for Balancer. These tokens serve several functions:

• Voting — holders decide on protocol parameters (fee levels, reward distribution, new pools)
• Liquidity incentives (liquidity mining) — protocol distributes governance tokens to LPs to attract TVL
• Value capture — a portion of fees goes to token holders (fee switch)

The ve-Token Model (Vote-Escrowed)

Curve Finance pioneered the ve-token model, which has become the standard for AMM protocols. The mechanics:

1. User locks CRV for a period from 1 week to 4 years, receiving veCRV
2. Longer lock = more votes and larger share of fees
3. veCRV holders vote on CRV reward distribution across pools (gauge voting)
4. Protocols “bribe” veCRV holders to direct rewards to their pools — hence the term “Curve Wars”

The Mercenary Capital Problem

Liquidity mining attracts capital, but this capital often leaves as soon as rewards end. Protocols lose TVL, and the governance token depreciates due to constant emissions. Solutions:

• Ve-model — token locking reduces circulating supply and sell pressure
• Protocol Owned Liquidity (POL) — the protocol itself owns liquidity instead of renting it
• Real yield — rewards paid from fees, not from emissions
• Performance-linked incentives — rewards proportional to trading volume, not just position size

Liquidity Design

For a tokenomist, an AMM is not a given — it’s a tool whose parameters must be designed. Key decisions at token launch:

Choosing the AMM and Pair

• Which blockchain? Ethereum (Uniswap, Curve), BNB Chain (PancakeSwap), Solana (Raydium), or multichain
• Which pair? TOKEN/ETH, TOKEN/USDC, or TOKEN/stablecoin — depends on the target audience
• Which model? Constant product for standard tokens, StableSwap for stablecoins, Weighted pool for launches via LBP
• Which fee tier? Uniswap V3 offers 0.01%, 0.05%, 0.3%, and 1% — volatile pairs benefit from higher fees

Initial Liquidity

Initial liquidity size determines market depth and acceptable slippage. Rule of thumb: slippage on a $10,000 trade should not exceed 1–2%.

For slippage under 2% on a $10,000 trade, you need a pool with at least $500,000 in reserves per token. This implies initial liquidity of $1,000,000+. For smaller projects, a realistic minimum is $50,000–200,000 with the understanding that large trades will have significant slippage.

Liquidity Incentive Programs

A typical liquidity mining program includes:

Incentive program parameters:

1. Budget:       5–10% of total token supply
2. Duration:     6–12 months with gradually decreasing rewards
3. Distribution: Proportional to LP's share of the pool
4. Decay:        −10 percentage points each quarter
5. Bonus:        Boosted rewards for the first 30 days

Example schedule (12 months, 8M token budget):
  Q1: 3.2M tokens (40%)
  Q2: 2.4M tokens (30%)
  Q3: 1.6M tokens (20%)
  Q4: 0.8M tokens (10%)

Protocol Owned Liquidity (POL)

POL is a model where the protocol itself owns liquidity in the pool rather than renting it from external LPs. Advantages:

• Sustainability — liquidity won’t leave when rewards end
• Revenue — protocol earns trading fees
• Control — can manage market depth and slippage
• No dilution — no need to emit tokens for incentives

Sources of POL: a portion of token sale proceeds (IDO, LBP), treasury revenue, bond mechanics (buying LP tokens at a discount from users). The ideal balance is POL as the liquidity base combined with an incentive program for additional TVL.

Trends

Concentrated Liquidity as the Standard

After Uniswap V3, concentrated liquidity became the industry standard. PancakeSwap, SushiSwap, and dozens of other AMMs adopted similar models. Automated position managers (Arrakis, Gamma) and yield optimizers (Beefy) emerged to rebalance ranges and auto-compound fees for LPs, lowering the entry barrier.

Uniswap V4 Hook Architecture

Uniswap V4 introduces hooks — custom smart contracts that execute before or after specific pool actions (swap, add/remove liquidity). This turns the AMM into a programmable platform:

• Dynamic fees — fees change based on volatility or volume
• TWAMM — execution of large orders at a time-weighted average price
• On-chain limit orders — automatically execute when the target price is hit
• Custom curves — any pricing formula, not just x*y=k
• KYC/permissioned pools — pool access only for verified addresses

The V4 singleton architecture (all pools in one contract, launched January 2025 on 10+ chains) reduces pool creation costs by ~99% and swap costs by ~30% (up to ~50% for multi-hop routes) compared to V3.

Intent-Based Trading

A new approach to decentralized trading: instead of interacting directly with a pool, the trader describes an intent — “I want to swap 1 ETH for the maximum amount of USDC.” A network of solvers then competes to fulfill this intent, finding the optimal route across multiple pools, bridges, and liquidity sources.

UniswapX, CoW Protocol, and 1inch Fusion already operate on this model. For LPs, this means competing not only with other pools but with off-chain market makers.

Cross-Chain AMMs

Liquidity remains fragmented across blockchains. Cross-chain AMMs (Thorchain, Chainflip) enable native asset swaps between networks without bridges, while cross-chain aggregators (Squid Router, Li.Fi) route trades through multiple liquidity sources and bridges.