Arbitrageurs' profits, LVR, and sandwich attacks: batch trading as an AMM design response

TL;DR

This work proposes a function-maximizing automated market maker (FM-AMM) that batches trades to enforce uniform pricing, thereby eliminating arbitrage profits and sandwich attacks that generate most MEV in CFAMMs. By showing that competition among arbitrageurs in the batched setting drives the executed price to the exogenous equilibrium, the FM-AMM transfers MEV gains from validators to liquidity providers and reduces adverse front-running. The authors derive the FM-AMM trading rule, connect it to a maximal-reserve-function objective, and analyze path-dependence and batching requirements, including a detailed empirical comparison using Binance data for 11 token pairs to benchmark LP returns against Uniswap v3. Results indicate FM-AMM LPs generally outperform Uniswap v3 across most pools, with the MATIC-ETH pair as an exception, and they explore the impact of fees and the presence of noise trading. The paper concludes that FM-AMMs offer a promising design to improve DeFi efficiency and reduce MEV, while highlighting practical considerations such as batch operator incentives and potential extensions to traditional finance contexts.

Abstract

We study a novel automated market maker design: the function maximizing AMM (FM-AMM). Our central assumption is that trades are batched before execution. Because of competition between arbitrageurs, the FM-AMM eliminates arbitrage profits (or LVR) and sandwich attacks, currently the two main problems in decentralized finance and blockchain design more broadly. We then consider 11 token pairs and use Binance price data to simulate the lower bound to the return of providing liquidity to an FM-AMM. Such a lower bound is, for the most part, slightly higher than the empirical returns of providing liquidity on Uniswap v3 (currently the dominant AMM).

Figures (8)

• Figure 1: Initially, the liquidity reserves of the CPAMM are $Y$ and $X$. A trader then purchases $x$ ETH at an average price $p(x)$. Note that, after the trade, the marginal price on the CPAMM (that is, the price for an arbitrarily small trade) is $\hat{p} \neq p^{CPAMM}(x).$
• Figure 2: On an FM-AMM, the price at which a given trade $x$ is executed equals the marginal price after the trade is executed. This implies that an FM-AMM "moves up" the curve with each trade.
• Figure 3: A positive-fee FM-AMM moves up the curve: effective price when the batch trades $x<0$, and there are no buy orders (in blue, the FM-AMM level curves for given $Y$ and $X$).
• Figure 4: Effective price when there are both buy and sell orders, for $x<0$, $x_{i'}>0$, and $x_{i"}<0$.
• Figure 5: Timeline

Theorems & Definitions (9)

• Definition 1: Constant Function Automated Market Maker
• Definition 2: Clearing-Price Consistent AMM
• Definition 3: Function-Maximizing AMM
• Proposition 1
• proof
• Proposition 2
• Proposition 3: FM-AMM is risk loving
• proof : Proof of Proposition \ref{['prop: main']}
• proof : Proof of Proposition \ref{['prop: risk loving']}