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Tight Characterizations of AMM Mechanism Design under Weak Efficiency
Chengkai Zhang, Lirong Xia, Elaine Shi, Mengqian Zhang, Qishen Han, Yuhao Li
TL;DR
Prior work leaves open whether AMMs can achieve incentive compatibility and weak local efficiency under plain consensus, where builders control transaction inclusion and ordering. This paper proves those guarantees incompatible for deterministic AMMs under stated conditions, separating censorship resilience from fair sequencing.
Problem
Whether incentive compatibility and weak local efficiency can be achieved under plain consensus remains open, despite the user harms associated with MEV.
Source: §1 · pp. 2–3Method
The paper establishes an impossibility result for deterministic AMMs under plain consensus, including when the consensus layer guarantees censorship resilience and block space is unlimited.
Source: §1.1 · p. 3Results
No deterministic AMM satisfying individual rationality, pricing curve conformity, and anonymity can achieve both incentive compatibility and weak local efficiency under plain consensus, even with censorship resilience and unlimited block space.
Source: §1.1 · p. 3Takeaways & Limitations
In this model, censorship resilience is weaker than fair sequencing for achieving incentive compatibility and weak local efficiency, which prior work achieves under fair sequencing.
Source: §1.1 · p. 3The proposed mechanism is substantially simpler than the stronger-efficiency alternative and is intended primarily to establish feasibility, not to offer an economically compelling design.
Source: §1.1 · p. 4
Abstract
from arXiv · showhide
Miner extractable value (MEV) poses a persistent challenge for blockchain ecosystems. It arises from the fact that a block builder can exploit its unilateral control over transaction inclusion and ordering to extract profit, potentially at users' expense. Recent work has explored consensus-aided mechanism design to mitigate MEV. This approach combines generic consensus-layer guarantees with application-layer mechanisms that use these guarantees to address application-specific MEV problems. Prior work exemplifies this approach for automated market makers (AMMs). When the consensus layer offers fair sequencing, which orders transactions according to their arrival times, their proposed mechanism achieves incentive compatibility (IC) and weak local efficiency (wLE). Informally, IC rules out profitable strategic deviations by users and builders. Meanwhile, wLE ensures that after execution, any order willing to trade at the initial price cannot benefit from further trade with the pool at the ending marginal price. In this work, we resolve the main open question left by prior works: whether IC and wLE can be achieved under plain consensus (e.g., current Ethereum) without fair sequencing. We prove that no deterministic, anonymous batch AMM can achieve both properties. The impossibility holds even when the consensus layer guarantees censorship resilience and block space is unlimited, establishing the first separation between censorship resilience and fair sequencing in the context of decentralized mechanism design. Our impossibility proof combines three strategic capabilities: creating Sybil identities, over-reporting budgets, and misreporting values. We further show the tightness of our impossibility result: removing any one from the strategy space restores feasibility under censorship resilience. Specifically, we construct a mechanism achieving IC and wLE for each restricted setting.
1 Introduction
MEV exploits builders’ control over transaction inclusion and ordering; prior AMM work achieves IC and wLE under fair sequencing. The introduction asks whether those guarantees can hold under plain consensus, then presents an impossibility result and restricted-strategy constructions.
1.1 Our Results and Contributions
- No deterministic, anonymous AMM satisfying individual rationality and pricing-curve conformity can achieve both IC and wLE under plain consensus, even with censorship resilience and unlimited block space.This resolves the open question left by prior work.Source: §1.1 · p. 3
- Under censorship-resilient consensus, retaining exact settlement makes IC incompatible even with wLE, motivating mechanisms that depart from exact settlement.The implication is stated to extend beyond the particular Otter construction [SZCL26].Source: §1.1 · p. 3
- The result separates consensus guarantees: IC and wLE are incompatible under censorship resilience, whereas prior work achieves both under fair sequencing.Fair sequencing orders transactions by arrival time and prevents builders from freely choosing their ordering.Source: §1 · p. 2, §1.1 · p. 3
- Removing any one of Sybil identities, aggregate budget over-reporting, or private values restores feasibility, with equal-share, proportional, and layered hand-in-hand mechanisms, respectively.The public-value setting still permits private budgets and unrestricted opposite-direction asks.Source: §1.1 · p. 4
- All three feasibility constructions combine initial-price matching across trade directions with a one-sided allocation rule tailored to the restricted setting.Eligible orders on the smaller-budget side trade their full budgets at the initial price; remaining orders use an augmented compensation curve.Source: §1.1 · p. 4
1.2 Additional Related Work
- Batch settlement can preserve the pool’s pricing curve after the batch, but the stronger guarantee of IC remains the question beyond prior work on arbitrage resilience.The paper also notes that fair sequencing, strategy-space restrictions, and surplus redistribution offer routes to feasibility.Source: §1.2 · p. 5
2 Model
The model specifies two-sided batch-AMM trading, the pricing curves and mechanism constraints, and the strategic actions available to users and builders. It defines incentive compatibility and weak local efficiency, then derives two implications of incentive compatibility under the model’s assumptions.
2 Model
- Sell-Y and sell-X users report a reservation value and budget for trading in opposite directions between the two assets.A sell-Y user's budget is in Y and value is measured in X; a sell-X user's budget is in X and value is measured in Y.Source: §2 · pp. 5–6
2.1 A Concave AMM Pricing Curve
- The pool uses increasing, concave compensation curves for both trade directions, with constant-product AMMs included as a special case.The curves are defined from the initial reserves and effective Y-payout capacity; their initial marginal prices are reciprocal.Source: §2.1 · p. 6
2.2 AMM Mechanism
- The batch mechanism assigns outcomes subject to reported-budget constraints, individual rationality, pricing-curve conformity, and anonymity.Pricing-curve conformity applies to aggregate batch outcomes, while anonymity bases outcomes on reported valuations, budgets, and relative order rather than identity.Source: §2.2 · p. 7
2.3 Strategy Space and Utility
- Users may misreport values and budgets, create identities, or submit orders in either direction; builders may reorder bids and inject Sybil bids.A builder-as-user may also misreport its valuation and budget, while the mechanism cannot identify which bids share an owner.Source: §2.3 · p. 7
2.4 Desired Properties
- IC requires truthful user reports and prescribed builder ordering to be dominant strategies, while wLE rules out beneficial additional trades for eligible bids at the final marginal price.Eligibility is based on asks no greater than the initial spot price; wLE evaluates the opportunity to trade directly with the pool after execution.Source: §2.4 · pp. 8–9
- Under reported-budget constraints, individual rationality, and pricing-curve conformity, IC implies that no order receives a positive amount without paying.The implication applies to sell-Y and sell-X orders in every report profile.Source: §2.4 · p. 9
- For deterministic anonymous AMMs satisfying builder IC, identical reports in a profile receive equal utilities evaluated at their common reported type.The result follows by considering a builder-as-user that swaps the positions of identical reports.Source: §2.4 · p. 9
3 Impossibility
The section establishes that incentive compatibility and weak local efficiency cannot both hold under the stated strategic capabilities, even with censorship resilience and unlimited block space. It develops structural results and uses loss bounds from a Sybil buyback deviation and a truthful profile to derive the incompatibility.
3 Impossibility
- No deterministic AMM can satisfy both IC and wLE when users may misreport values and budgets, create finite Sybils, and builders may reorder—even with censorship resilience and unlimited block space.The model also requires individual rationality, pricing-curve conformity, and anonymity.Source: §3 · p. 10
3.1 Notations and Useful Observations
- For a sell-Y order reporting value v and budget q, IC and wLE imply its outcome matches a zero-value report with budget equal to its realized sale.Its utility must also be at least the utility from any zero-value report with budget s ≤ q; the same result applies with X and Y exchanged.Source: §3.1 · p. 11
3.2 Trading at the Initial Price
- When all reported values are strictly below the initial price, every order on the smaller-total-budget side spends its full budget and trades at the initial price.With equal total budgets, all orders spend their full budgets at the initial price and the pool is unchanged; the paper identifies this characterization as a central technical contribution.Source: §3.2 · pp. 13, 15
3.3 The Sybil Deviation and the Contradiction
- The section defines a sell-Y order’s loss as the Y it spends minus the X it receives, measuring its shortfall relative to exchange at the initial price.This definition introduces the loss measure used in the subsequent two-order bound.Source: §3.3 · p. 15
- A Sybil buyback deviation bounds the two sell-Y orders’ losses by c1 ≤ 2C(a)/3 and c2 ≥ C(a)/3.The deviating user replaces one sell-Y order with two sell-Y identities and a buyback order; symmetry gives each identical sell-Y order an equal receipt.Source: §3.3 · pp. 15–16
- The loss bounds imply F(a) = a − C(a) ≥ a/2, while the pool’s payout bound gives a < 2K.These bounds contribute to the contradiction between the utilities required by truthful reporting and the utilities allowed by the truthful profile.Source: §3.3 · pp. 16–17
- The truthful profile requires U1 + U2 > 16K under incentive compatibility, but its combined utility expression contradicts that bound for K > 0.The combined utility is εR + F(z) − vz.Source: §3.3 · p. 17
4 Feasibility Results
This section establishes feasibility results for restricted strategy settings, showing how hand-in-hand and layered mechanisms can satisfy incentive-compatibility and allocation guarantees under stated restrictions on identities, budget reports, and value or direction reports.
4.1 A Shared Two-Sided Matching Construction
- The shared construction matches eligible orders at the initial price on the smaller-budget side, then applies a one-sided rule to the remainder on an augmented compensation curve.Lemma 10 guarantees that the resulting two-sided mechanism satisfies reported-budget constraints, individual rationality, pricing curve conformity, anonymity, weak local efficiency, and a portfolio price bound.Source: §4 · p. 17, §4.1 · p. 20
4.2 No Sybil Identities: The Hand-in-Hand Mechanism
- With at most one identity per user, the hand-in-hand mechanism is incentive compatible and also satisfies the properties guaranteed by Lemma 10.Those properties include weak local efficiency, individual rationality, pricing curve conformity, and anonymity.Source: §4.1 · p. 20, §4.2 · p. 21
4.3 No Budget Over-Reporting: Proportional Hand-in-Hand
- On a fixed curve, proportional hand-in-hand is incentive compatible against same-direction deviations that do not over-report aggregate budget.The rule divides marginal transactions among active orders in proportion to remaining budgets; users may split or under-report budgets, but cannot exceed their true aggregate budget in their true trading direction.Source: §4.3 · pp. 22–23
- The two-sided proportional hand-in-hand mechanism is incentive compatible under (19), including against finite collections of identities in both directions, and satisfies the properties of Lemma 10.Its settlement requirements hold and its updates depend only on reported asks and remaining budgets, establishing anonymity.Source: §4.3 · p. 25
- Under the same reporting restrictions, bid-order-independent outcomes and the portfolio price bound rule out risk-free profit from a builder’s injected orders.For a builder without intrinsic trading demand, a strict net gain in either token requires a net loss in the other.Source: §4.3 · p. 25
4.4 Public Values: A Layered Mechanism
- With true-direction values public and budgets private, the common-value rule satisfies one-sided settlement and linear completion, and truthful users cannot gain from budget misreports or same-value Sybils when realized input respects their true budget.The rule also satisfies weak local efficiency and anonymity.Source: §4.4 · p. 26
- The layered rule makes active asks an initial segment, fully spends every active layer below the highest active ask, and satisfies settlement, anonymity, weak local efficiency, and linear completion.Linear completion is established when the curve has an initial linear segment and all input asks are at most its slope.Source: §4.4 · p. 28
- For public value v in [0, σ0], extending initial-price crossing and budget by d raises truthful utility by at most (σ0 − v)d.This bound also covers a layer that was inactive before the prefix was extended.Source: §4.4 · pp. 29–30
- The combined two-sided mechanism is incentive compatible under the stated public-value strategy restriction and satisfies the properties in Lemma 10.It combines the initial-price matching construction with the one-sided public-value layered mechanism.Source: §4.4 · p. 30
- The strategy restriction allows finite identity collections in both directions and aggregate budget over-reporting, with no restriction on opposite-direction asks.Source: §4.4 · p. 30
- For sell-Y deviations that make sell-Y the majority, realized input is bounded by q + d, yielding utility at most T(M + d; v, q + d) − (σ0 − v)d ≤ T(M; v, q).Exchanging X and Y extends the argument to true sell-X users.Source: §4.4 · pp. 30–31
- When sell-X becomes the majority, crossing-prefix, initial-price, and portfolio bounds control deviations even if declared sell-Y budget b exceeds q; only net realized expenditure is constrained.Source: §4.4 · pp. 30–31
AI Acknowledgements
The work began in December 2025, with the authors developing the shared matching construction, two mechanisms, and an initial impossibility result. ChatGPT 5.6 and ChatGPT-6-Astra later contributed to the public-value mechanism and the wLE impossibility proof; the authors reviewed and substantially revised AI-generated text.
AI Acknowledgements
- The authors developed the shared two-sided matching construction and the mechanisms for settings without Sybil identities and without aggregate budget over-reporting.Source: AI Acknowledgements · p. 31
- The authors initially proved impossibility under a stronger efficiency requirement than weak local efficiency (wLE).Source: AI Acknowledgements · p. 31
- ChatGPT 5.6 developed the public-value mechanism, and ChatGPT-6-Astra later established impossibility under wLE; the authors reviewed and substantially revised all AI-generated text.Source: AI Acknowledgements · p. 31