A Trilemma in AMM Mechanism Design

2026-05-26

AI Summary

This study investigates the adverse price impacts in automated market maker (AMM) mechanisms caused by miner-extractable value (MEV), focusing on whether incentive compatibility (IC), weak local efficiency (wLE), and uniform pricing (UP) can coexist. Leveraging mechanism design theory and formal analysis under standard blockchain consensus assumptions, the work models AMM trading behavior and establishes—rigorously and for the first time—the “AMM trilemma” theorem: any two of these three properties can be simultaneously satisfied, but all three cannot hold together. This result uncovers a fundamental trade-off inherent in MEV-resistant AMM design and delineates theoretical boundaries that inform future mechanism improvements.

Abstract

Blockchains have popularized the Automated Market Makers (AMMs), where users trade crypto-assets directly with a smart contract, governed by a pricing function embedded in the contract's code. Today, users of AMMs are often forced to accept unfavorable prices due to widespread front-running and back-running attacks, commonly known as Miner Extractable Value (MEV). Several earlier works show impossibility results suggesting that completely removing MEV at the consensus layer is impossible, partly because the consensus layer is agnostic of application-level semantics. For this reason, more recent works have advocated mechanism design approaches at the application (i.e., smart contract) level. We study a natural two-asset AMM mechanism design problem recently initiated and explored in prior work by Chan, Wu, and Shi, in which they proposed a mechanism that satisfies a surprisingly strong notion of incentive compatibility (IC), under the consensus assumption that the underlying blockchain provides sequencing fairness. In this paper, we investigate the (in)feasibility of simultaneously achieving IC and other desirable properties such as weak local efficiency (wLE) and uniform pricing (UP). At a high level, wLE requires that the mechanism should not leave any unfulfilled demand from users whose asking prices are not overly restrictive, and whose orders could have been executed directly against the pool. UP requires that all orders that get (partially) executed must trade at the same exchange rate. We unveil the underlying mathematical structure of AMM mechanism design, and our main results can be summarized as a trilemma-style theorem: among the desirable properties IC, wLE, and UP, any two out of three are possible, but no mechanism can satisfy all three.

Problem

• Automated Market Makers
• incentive compatibility
• weak local efficiency
• uniform pricing
• MEV

Innovation

• Automated Market Maker
• Incentive Compatibility
• Miner Extractable Value
• Mechanism Design
• Trilemma