Uniform-Price Mechanism Design for Automated Market Makers

Abstract

Automated market makers (AMMs) are central to decentralized exchanges, but their reserve curves make mechanism design different from classical double auctions. We study a batch double auction with buyers, sellers, and a liquidity-nondecreasing AMM: post-trade reserves must have weakly larger product than the initial reserves. Each user has two-dimensional private information: a unit value and a demand or supply quantity. User trades clear at one uniform price subject to AMM feasibility. The objective is user-side trading volume, benchmarked against the optimal feasible individually rational (IR) uniform-price allocation. We give a randomized uniform-price mechanism based on binary quantity buckets. It randomly chooses one of three clearing modes: peer-to-peer matching, AMM sales to buyers, and seller sales to the AMM. Every deterministic realization of the mechanism is ex-post feasible and satisfies IR and weak quantity incentive compatibility: conditional on any quantity report, truthful unit-value reporting is dominant whenever it gives a non-negative utility, no unit-value deviation gives a positive utility if the truthful one doesn't, and users cannot benefit by under-reporting the quantity together with their truthful unit value. Let $V^\ast$ be the optimal feasible IR uniform-price volume without incentive constraints, and let $γ=\bar q/\underline q$, where $\bar q$ and $\underline q$ are the quantity-domain bounds. For $γ\ge1$, the mechanism achieves an expected trading volume of $ Ω(1/(1+\logγ)^2)V^\ast - O(\bar q). $ We also show that full incentive compatibility over the two-dimensional type space forces a worst-case approximation ratio of $O(1/γ)$ at every prescribed initial reserve ratio, even when both AMM reserves are scaled by an arbitrarily large common factor and the optimal volume $V^\ast$ is arbitrarily large relative to $\bar q$.