Source-linked AI summary
am-AMM: An Auction-Managed Automated Market Maker
Austin Adams, Ciamac C. Moallemi, Sara Reynolds, Dan Robinson
TL;DR
AMM design must address losses to informed arbitrageurs while optimizing fees for retail flow, a difficult and often static choice for liquidity providers. The am-AMM uses an auction to select a pool manager who can set fees and capture some arbitrage. Under certain assumptions, it attracts more liquidity in equilibrium than any fixed-fee constant-product AMM pool with a fee up to the cap.
Problem
AMM design must reduce losses to arbitrageurs while optimizing fee revenue from retail flow, but liquidity providers face a difficult static fee choice.
Source: §1 · pp. 1–2Method
The am-AMM uses a censorship-resistant onchain auction to select a manager who sets the swap fee, collects swap fees, and can capture small arbitrage opportunities.
Source: §1 · p. 2Results
Under certain assumptions, the am-AMM attracts more liquidity in equilibrium than any fixed-fee constant-product AMM pool with a fee up to the cap.
Source: §1 · p. 2Takeaways & Limitations
The design shifts the strategic burden of setting fees from passive liquidity providers to a manager assumed to be more sophisticated and able to model trader sensitivity and arbitrage losses.
Source: §5 · p. 12The manager’s zero-fee trading can worsen sandwich attacks, potentially hurting swappers or discouraging retail flow and undermining the assumption that retail flow depends only on liquidity and fees.
Source: §5 · p. 12
Abstract
from arXiv · showhide
Automated market makers (AMMs) have emerged as the dominant market mechanism for trading on decentralized exchanges implemented on blockchains. This paper presents a single mechanism that targets two important unsolved problems for AMMs: reducing losses to informed orderflow, and maximizing revenue from uninformed orderflow. The ``auction-managed AMM'' works by running a censorship-resistant onchain auction for the right to temporarily act as ``pool manager'' for a constant-product AMM. The pool manager sets the swap fee rate on the pool, and also receives the accrued fees from swaps. The pool manager can exclusively capture some arbitrage by trading against the pool in response to small price movements, and also can set swap fees incorporating price sensitivity of retail orderflow and adapting to changing market conditions, with the benefits from both ultimately accruing to liquidity providers. Liquidity providers can enter and exit the pool freely in response to changing rent, though they must pay a small fee on withdrawal. We prove that under certain assumptions, this AMM should have higher liquidity in equilibrium than any standard, fixed-fee AMM.
1. Introduction
AMM liquidity providers face two linked challenges: limiting arbitrage losses while setting fees that capture retail demand without fragmenting liquidity. The auction-managed AMM combines arbitrage capture and market-set fees, and under certain assumptions attracts more liquidity than any fixed-fee constant-product pool.
1. Introduction
- Fixed-fee AMMs force LPs to balance arbitrage protection against retail fee revenue; differing static fee choices can fragment liquidity, while retail demand and optimal fees may vary with market conditions.Dynamic-fee approaches exist, but the paper describes the am-AMM as a first attempt at a provably incentive-compatible fee set by the market to attract more liquidity than fixed-fee AMMs.Source: §1 · pp. 1–3
- Under certain assumptions, the am-AMM attracts more liquidity in equilibrium than any fixed-fee constant-product AMM pool with a fee up to the cap.The design targets both loss-vs-rebalancing reduction and fee optimization through one mechanism.Source: §1 · p. 2
- Unlike standard fixed-fee AMMs, the am-AMM targets both arbitrage losses and retail-fee optimization, while making pool liquidity tradeable with a capped fee even when the manager has not submitted a transaction.The proposal extends the “MEV capturing AMM” (McAMM) idea to let the manager set and collect retail fees, and guarantees accessibility.Source: §1 · pp. 2–3
- A censorship-resistant onchain auction selects a manager who sets the swap fee, receives pool fees, and can capture small arbitrage opportunities by trading effectively without fees.The am-AMM is constant-product; liquidity providers can enter and exit freely, subject to a small withdrawal fee.Source: §1 · p. 2
- The design may offer weaker protection against sandwich attacks than fixed-fee AMMs, could contribute to block-builder centralization, and leaves concentrated-liquidity integration for future study.The manager’s ability to trade without fees is the stated source of sandwich-attack concern.Source: §1 · p. 2
2. Auction Design
The auction uses delayed rent bids to assign a pool manager while allowing liquidity providers time to react to rent changes. A small withdrawal fee or delay limits strategic exits around arbitrage opportunities.
2. Auction Design
- A Harberger lease is a continuously held English auction with bids expressed as rent per block, and the top active bid determines the manager who pays rent to LPs.Rent is paid in pool tokens to LP token holders proportional to their stake, so it compounds automatically.Source: §2 · p. 3
- Bids specify per-block rent and a deposit of at least R · K; new bids activate after K blocks, and a minimum bid increment applies.A top bid cannot be canceled, and its deposit must remain sufficient to cover the K-block rent requirement.Source: §2 · pp. 3–4
- The manager sets the next block’s swap fee up to fmax and receives all swap fees, enabling zero-fee trading that captures small price-movement arbitrage; larger moves can leave profit to others.The larger-move case occurs when price moves beyond the current fee, outside the “no-trade region.”Source: §2 · p. 4
- The delay parameter K is chosen so censoring the base layer for K consecutive blocks is negligibly likely, preventing manager usurpation and giving LPs time to respond to rent changes.Both the rent and manager for block N are locked in as of block N − K.Source: §2 · pp. 3–4
Withdrawal fees.
- LPs may enter or exit at any time, but a small withdrawal fee paid to the manager prevents exits after volatility is realized from reducing the manager’s assumed arbitrage profit.With a 1% fee cap, a withdrawal fee below 0.13 basis points can suffice; a withdrawal delay could have a similar effect.Source: Withdrawal fees · p. 4
3. Theory
The theory models liquidity providers’ fee income and arbitrage losses, then compares competitive liquidity under fixed-fee and auction-managed AMMs. Under the stated assumptions, the auction-managed AMM has higher equilibrium liquidity than any fixed-fee AMM.
3. Theory
- The model treats noise traders as fee-generating demand and arbitrageurs as a source of adverse-selection costs to liquidity providers.Noise-trader volume decreases with fees and is satiated as liquidity grows; arbitrage profits scale linearly with pool value and decrease with fees.Source: §3 · pp. 5–6
3.1. Fixed-Fee AMM Model
- In the fixed-fee benchmark, liquidity providers’ expected return combines noise-trader fee revenue, arbitrage losses, and a capital charge; free entry yields a unique zero-profit equilibrium liquidity for each fee.The capital charge is the risk-free rate.Source: §3.1 · p. 7
3.2. Auction-Managed AMM Model
- In the am-AMM, the manager chooses the fee to maximize fee revenue adjusted for arbitrage excess, while rent paid by the manager contributes to liquidity providers’ returns.The manager effectively trades without fees; the theorem also gives an equilibrium fee and liquidity under zero-profit conditions.Source: §3.2 · pp. 7–9
- Theorem 1 establishes that equilibrium liquidity in the am-AMM exceeds that of every fixed-fee AMM.The result follows under the paper’s equilibrium conditions and model assumptions.Source: §3.2 · pp. 8–9
- Under concave fee revenue and convex arbitrage excess, the am-AMM’s equilibrium fee is at least the fee that solely maximizes noise-trader revenue.When arbitrage excess at the revenue-maximizing fee is very small, the equilibrium fee may remain nearly optimal for noise-trader revenue.Source: §3.2 · p. 9
4. A Structural Model for Arbitrageur Excess
The structural model derives arbitrageur excess under a setting with stochastic asset prices and block times. It finds that excess is smaller because arbitrageurs are less likely to trade after the pool manager resets mispricing at each block.
4. A Structural Model for Arbitrageur Excess
- The structural setup models the asset price as geometric Brownian motion and block arrivals as a Poisson process, with a symmetry assumption making log-mispricing driftless.The fee is approximated by the parameter γ for comparison with Milionis et al. (2023).Source: §4 · pp. 9–10
- The derivation combines the expected profits from trades by outside arbitrageurs who reduce mispricing to the fee level before the manager trades.The paper states the derived expression applies when ∆t < 8σ^2.Source: §4 · pp. 10–11
- Arbitrageur excess is lower than total arbitrage profits because the probability of an outside arbitrage trade is exponentially smaller, while expected profit conditional on trading is the same.The pool operator corrects mispricing at each block, making large mispricings at the next block’s start unlikely.Source: §4 · p. 12
5. Discussion
The am-AMM shifts fee-setting from passive liquidity providers to a pool manager, while its zero-fee arbitrage trading can improve quoted prices. The discussion also identifies risks involving sandwich attacks, block building, fee incentives, and the model’s scope.
Advantages
- The manager sets fees to optimize noise-trader revenue, shifting the strategic burden from passive liquidity providers to a more sophisticated participant.The manager’s fee choice accounts for arbitrage excess paid to arbitrageurs and can use off-chain modeling of noise-trader sensitivity and arbitrage losses.Source: §5 · p. 12
- The manager’s zero-fee arbitrage trades can correct smaller price discrepancies, making quoted prices more accurate than in a fixed-fee AMM.The model captures fee and liquidity as drivers of noise-trader demand, while the discussion notes that noise traders may also care about relative mispricing.Source: §5 · p. 12
- LPs receive ex ante rent instead of lumpy, stochastic swap-fee revenue, transferring revenue risk to the manager.The authors suggest this transfer may improve welfare because managers may be larger, better capitalized, and less risk averse than typical passive LPs; the analysis assumes risk neutrality.Source: §5 · p. 12
Drawbacks
- A zero-fee manager can profit by pushing publicly visible swaps to their limit price, potentially harming swappers or discouraging retail flow.The authors note that this may undermine the model’s assumption that retail flow depends only on liquidity and fees; they mention verifiable sequencing rules, private relays, and offchain filler auctions as possible mitigations.Source: §5 · pp. 12–13
- The auction may affect block building: exclusive arbitrage rights could advantage the manager, while sophisticated parties or those with private orderflow may be more likely to win.The authors also note that capturing arbitrage could reduce block proposers’ power, and say these possible consequences warrant further study.Source: §5 · p. 13
- Unlike McAMM, the manager does not capture arbitrage excess from single-block price moves beyond the no-trade region, encouraging fees above the total-revenue optimum.Requiring the manager to unlock the pool every block could address this incentive, but would sacrifice accessibility.Source: §5 · p. 13
Future work
- The analysis focuses on constant-product AMMs; extending the design to concentrated-liquidity AMMs remains future work.The discussion also leaves heterogeneous LP returns and out-of-range liquidity under price changes for future work.Source: §5 · p. 13
- Implementing the mechanism is left for future work, though the discussion notes a third-party open-source implementation, BidDog (2024).Source: §5 · p. 13
A. Proofs
The proofs establish equilibrium existence and compare the am-AMM’s equilibrium liquidity with the fixed-fee benchmark. They show that its equilibrium liquidity exceeds the maximum liquidity achievable by a fixed-fee AMM.
Equilibrium existence
- For the fixed-fee case, continuity and the stated limiting behavior of G(L) yield an equilibrium, which is unique because G is strictly monotonic.Source: A. Proofs · p. 15
- For the am-AMM, continuity and the limiting behavior of G(L) imply that an equilibrium (R*, L*) exists.Source: A. Proofs · p. 15
Comparison with fixed-fee AMM
- The proof compares the am-AMM with the fixed-fee benchmark using Lmax and the fee f* that maximizes fixed-fee liquidity.Source: A. Proofs · p. 15
- Equilibrium am-AMM liquidity L* exceeds Lmax, the maximum liquidity achievable in the fixed-fee AMM.At rent Rmax, the manager earns positive profits, so equilibrium rent must exceed Rmax and equilibrium liquidity must exceed Lmax.Source: A. Proofs · pp. 15–16
B. Withdrawal Fees
The withdrawal fee is designed to keep strategic LP withdrawals from reducing a manager’s profit after volatility creates an arbitrage opportunity. Under the stated example, the required fee is small when the fee cap is 1%.
Withdrawal fee
- With a 1% fee cap, the example gives a withdrawal fee of about 0.1238 basis points, or $12.38 on a $1 million position.The passage also reports this as approximately 0.00001238%.Source: B. Withdrawal Fees · p. 16
Purpose and condition
- The fee is intended to prevent LPs from withdrawing after volatility is realized but before the manager can execute an arbitrage.Under the stated assumptions, the manager’s profit from an opportunity is capped once price moves by fcap; larger moves leave excess MEV to the block proposer.Source: B. Withdrawal Fees · p. 16
Fee condition
- The required fee need only exceed the value of arbitraging the liquidity after an increase by a factor of fcap; a decrease by that factor creates a smaller opportunity.Source: B. Withdrawal Fees · p. 16