Source-linked AI summary
Otter: A Provably MEV-Resilient Automated Market Maker via Surplus Redistribution
Elaine Shi, Mengqian Zhang, Hao Chung, Yuhao Li
TL;DR
MEV lets block builders profit by controlling transaction ordering and injected trades, imposing user costs and contributing to centralization. Otter is a two-asset AMM designed for censorship-resilient consensus and uncongested block space, and it provides truthful, strategy-proof trading with strong social-welfare guarantees.
Problem
MEV lets block builders exploit transaction inclusion and ordering, imposing costs on users and creating forces toward builder centralization.
Method
Otter is a computationally efficient two-asset AMM that uses surplus redistribution and assumes censorship resilience at the consensus layer.
Results
Otter makes truthful reporting optimal for users and builders, prevents profitable builder manipulation including reordering and sybil bids, and maximizes social welfare in a strong sense.
Takeaways & Limitations
The mechanism removes incentives for strategic trading and builder manipulation, including when the builder itself has intrinsic demand to trade.
Takeaways & Limitations
Pareto optimality cannot be achieved under the stated incentive-compatibility notions when non-eligible users are included, so the analysis excludes them.
Abstract
from arXiv · showhide
Miner extractable value (MEV) in automated market makers allows block builders to profit from transaction ordering and injected trades, imposing costs on users and contributing to builder centralization. We introduce Otter (Optimal Truthful Trading with Excess Redistribution), a two-asset batch AMM that achieves provable MEV resilience when the consensus layer provides censorship resilience and block space is uncongested. Otter makes truthful behavior a dominant strategy for both users and builders. Consequently, a builder cannot profit from strategic deviations, including reordering bids or injecting sybil bids, even when the builder is itself a trader with intrinsic value. Moreover, we show that Otter maximizes social welfare, in a strong sense, within a natural class of mechanisms satisfying the desired game-theoretic properties. To achieve these guarantees, we introduce a new paradigm called surplus redistribution, which provably prevents residual surplus from being captured as MEV by redirecting it to the broader community. Specifically, the pool's output tokens need not be distributed entirely among users in the current batch. Instead, residual surplus may be transferred to a smart contract governed by the decentralized community. The accumulated surplus can be used to benefit community members --- for example, by subsidizing transaction fees, rewarding liquidity providers, or returning assets to the pool. Our approach relies on the underlying consensus layer to provide censorship resilience. We motivate its necessity through an impossibility result showing that the desired game-theoretic guarantees become unattainable when the builder is additionally allowed to censor transactions. Thus, our results also provide a mathematically formal demonstration of how consensus-level security guarantees can fundamentally expand what is achievable at the application layer.
1 Introduction
Otter addresses MEV in AMMs with a two-asset mechanism that makes truthful participation optimal and redirects residual surplus to the broader community. Its guarantees depend on censorship-resilient consensus and uncongested block space, while censorship enables an impossibility result.
- Motivation: MEV attacks in AMMs let strategic builders profit from transaction ordering and injected trades at ordinary users’ expense.Sandwich attacks can force users to trade at the worst price allowed by their slippage tolerance.
- Otter: Otter provides provable MEV resilience under censorship-resilient consensus and uncongested block space.The mechanism remains order-independent and protects against builder misreporting, transaction reordering, and sybil bids.
- Incentives: Truthful reporting and sybil-proofness hold for users, builders, and builders-as-users, even after observing other bids.The mechanism removes strategic advantages from delaying bids and injecting pseudonymous identities.
- Efficiency: Otter maximizes social welfare in a strong sense at equilibrium because truthful behavior is an equilibrium for users, builders, and builders-as-users.This guarantee is stated alongside the mechanism’s strategy-proofness properties.
- Surplus redistribution: Surplus redistribution prevents residual pool output from being captured as MEV by transferring it for the benefit of the broader decentralized ecosystem.The surplus can support community uses such as reducing users’ effective trading costs, rewarding liquidity providers, or returning assets to the pool.
- Consensus-layer assumption: If block space is finite and builders can censor bids, no non-trivial AMM can guarantee both truthful users and strategy-proof builder-as-users.The result formally separates application-layer guarantees achievable with censorship resilience from those achievable without it.
2 Model
The model represents two-sided trading through sell-Y and sell-X orders, a concave AMM pricing curve, and strategic users and builders who may misreport, reorder, or inject bids. It evaluates incentive compatibility, feasibility, and efficiency while accounting for surplus redistributed to the community.
- Orders: Users submit sell-Y or sell-X orders that exchange one token for the other subject to declared budget caps.Sell-Y orders obtain X for Y, while sell-X orders obtain Y for X.
- Desired properties: Surplus compensation tokens may be burnt and redistributed to the decentralized community, so feasibility requires no outside subsidy.The model defines social welfare using X as numeraire and includes the effectively redistributed burnt amount.
- Strategy space: Strategic users and builders may misreport values or budgets, create sybil identities, and, for builders, reorder bids.A builder-as-user may also misreport intrinsic demand; the mechanism observes declared identities rather than real ownership.
- Pricing curve: The AMM uses increasing, concave one-sided compensation curves derived from a signed pricing curve F and its inverse-direction curve H.The initial marginal compensations are σ0 = F′(0) for sell-Y and ρ0 = 1/σ0 for sell-X.
- Desired properties: Order-insensitivity plus UIC implies strategy-proofness for the builder or builder-as-user, while UIC also yields no free lunch under zero-budget normalization.The mechanism gives zero allocation and compensation to truthful zero-budget reports.
- Desired properties: The mechanism’s target properties include individual rationality, feasibility, UIC, builder strategy-proofness, and Pareto optimality for eligible bids.A bid is eligible when its ask is no greater than the initial spot compensation; Pareto optimality cannot extend to non-eligible users under the incentive requirements.
3 Warmup: A One-Sided VCG Auction
The one-sided warmup constructs a VCG auction that maximizes welfare by allocating along the AMM curve to the lowest-ask sellers and compensating them with Clarke pivot payments. Its efficient implementation is sorting-based and preserves the welfare-maximizing allocation while satisfying key incentive and feasibility properties.
- Setup: The one-sided construction permits only sell-Y bids, with the sell-X case defined symmetrically.It applies more generally to any compensation curve satisfying the stated one-sided conditions.
- Allocation rule: The allocation rule maximizes welfare, then maximizes total Y sold among welfare maximizers before applying exogenous tie-breaking.Each seller receives an allocation y_i* under this rule.
- Compensation rule: The compensation rule gives each seller a Clarke pivot payment consisting of the AMM cost plus a rebate equal to the welfare increase caused by that seller.The rebate is determined after the efficient allocation is computed.
- Efficient implementation: The marginal-auction implementation repeatedly serves the lowest ask while marginal compensation covers marginal cost, stopping at a welfare maximizer.Concavity makes marginal output nonincreasing, while aggregate supply costs have nondecreasing marginal asks.
- Efficient implementation: O(|S| log |S|) comparisons suffice after sorting users by nondecreasing ask, with O(|S|) pricing-curve crossing points computed.The procedure stops when the next ask exceeds the current marginal price.
- Efficient implementation: The efficient implementation produces exactly the same allocation as the social-welfare maximizer in Equation (3).The equivalence is stated as Fact 11.
- Guarantees: The one-sided VCG auction is well-formed, individually rational, feasible, welfare-submodular, and user incentive compatible.These properties are collected in Theorem 12.
4 The Full Two-Sided Mechanism
The full mechanism extends the one-sided VCG auction to both trading directions by identifying a dominant side and modifying its compensation curve to incorporate eligible opposite-side liquidity. Under the pricing-curve assumptions, it satisfies the paper’s principal incentive, feasibility, and efficiency guarantees.
- Dominant-side selection: The mechanism filters ineligible bids, compares spot-eligible supply on both sides, and designates the side with greater spot-equivalent supply as dominant.Ties are resolved in favor of the sell-Y direction.
- Sell-Y dominant: When sell-Y is dominant, all eligible sell-X orders execute at the initial spot price and the sell-Y side uses a modified curve with an initial flat-price region.The first M = ρ0DX units of Y receive the initial spot price before the original curve applies to excess Y.
- Curve construction: The modified compensation curves remain increasing and concave, preserving the one-sided auction conditions in the two-sided construction.For the sell-Y-dominant case, this is stated directly after extending F; the sell-X case is symmetric.
- Coverage: QY ≥ M for sell-Y users and QX ≥ M for sell-X users, ensuring the dominant-side allocation covers the opposite-side spot-eligible supply.These bounds are stated in Facts 13 and 14.
- Sell-X dominant: When sell-X is dominant, the mechanism symmetrically executes eligible sell-Y orders at the initial spot price and runs one-sided VCG on sell-X orders.Minority-side trades supply DX units of X and require exactly M units of Y as compensation.
- Main guarantee: The full two-sided mechanism is well-formed, individually rational, feasible, UIC, strategy-proof against builders and builder-as-users, and Pareto optimal for eligible users.These guarantees require the pricing curve to satisfy assumptions (A1)–(A4).
5 Proofs for the Two-Sided Mechanism
The two-sided mechanism establishes feasibility, Pareto optimality, and incentive compatibility across both dominance regimes. Its proofs also rule out beneficial cross-direction sybil attacks, including for builder-as-users.
- Feasibility and Pareto optimality: Residual dominant-side input is sent to the pool after minority compensation, while compensation payments remain fully funded.In the sell-Y-dominated case, residual input is y = QY − M ≥ 0, and the pool returns F(y) units of X.
- Feasibility and Pareto optimality: No subset of eligible users can make an additional admissible trade after eligible minority-side sell-X users exhaust their input budgets.Any further trade would require both an X supplier and a Y supplier, which are unavailable within the eligible subset.
- Feasibility and Pareto optimality: Additional trades with the pool cannot strictly improve an underfilled dominant-side user’s utility because pool output is no greater than the reported cost of extra input.This establishes Pareto optimality in the sell-Y-dominated profile, with the opposite case following symmetrically.
- Incentive compatibility: User incentive compatibility suffices for builder-as-user strategy-proofness because the mechanism is insensitive to order.The sybil analysis shows that arbitrary finite cross-direction sybil attacks do not benefit a true sell-Y user.
- Feasibility and Pareto optimality: Minority-side users receive compensation at the initial spot price and strictly eligible orders exhaust their reported budgets.The result is established symmetrically for sell-Y- and sell-X-dominated profiles.
- Incentive compatibility: At equality between dominance conditions, the reverse branch is sell-Y dominated, and the proof carries over with adjusted weak and strict inequalities.Spot-eligible sell-X sybils execute fully at the spot rate, while ineligible sell-X sybils execute zero.
6 Social Welfare Maximization
The mechanism’s welfare guarantees follow from structural constraints imposed by naturalness, user incentive compatibility, and Pareto optimality. Within this class, it equalizes minority-side truthful utility and maximizes dominant-side welfare.
- Natural mechanisms: Natural mechanisms drop ineligible bids, prohibit price reversal, and impose no directional reversal in residual pool trades.The final marginal price moves weakly against the dominant side.
- Minority-side execution: Every executed minority-side order is compensated at the initial spot price, and strictly below-spot asks exhaust their reported budgets.This structure follows from UIC and Pareto optimality for eligible users.
- Welfare definition: The minority side receives exactly M units of the compensation token, while dominant-side expenditure beyond M becomes residual pool input.The dominant-side welfare objective counts crossed output plus pool output minus reported production cost.
- Welfare maximality: Among deterministic natural mechanisms satisfying UIC and Pareto optimality, Otter gives strictly eligible minority users the same truthful utility as every mechanism in the class.Boundary and ineligible minority-side users receive zero.
- Welfare maximality: Otter maximizes dominant-side welfare: DSWY in sell-Y-dominated profiles and DSWX in sell-X-dominated profiles.The comparison uses the mechanism’s larger crossing length and concavity of the pool curve.
- Efficiency requirements: Theorems 17 and 18 remain valid when Pareto optimality is weakened to weak local efficiency.The proofs only require ruling out profitable additional trades between eligible users and the pool.
7 Restrictions on Builder Fee Structure
The builder-fee analysis shows that incentive compatibility for users and builder-as-users uniquely forces residual surplus away from builders. The resulting structure permits community redistribution but not outcome-dependent builder fees.
- Fee structure: The mechanism burns unused compensation tokens rather than paying outcome-dependent fees to the builder.A constant exogenous block subsidy remains compatible with the game-theoretic guarantees.
- Scope of impossibility: The zero-fee impossibility already holds on finite sell-Y-only profiles using only valuation misreports.Therefore enlarging the profile and strategy spaces does not restore a positive builder fee.
- Accounting constraint: Feasibility imposes an accounting constraint requiring user compensation, builder fees, and burns to be funded by pool output.For randomized mechanisms, the proof uses expected values and concavity via Jensen’s inequality.
- Payment uniqueness: Seller payment uniqueness implies that two truthful compensation rules for the same spending rule can differ only by a report-independent constant.The result applies to expected spending and compensation in randomized mechanisms.
- Zero builder fees: Under IR, feasibility, UIC, and builder-as-user strategy-proofness, the expected builder fee is zero for every report profile.Because builder fees are nonnegative, zero expectation forces the fee to be zero with probability one.
8 Impossibility with Censorship
Allowing a builder to censor bids in a finite-capacity block makes the desired incentive guarantees impossible for any non-trivial anonymous AMM. The proof exploits many low-ask identities and a profitable censorship substitution.
- Censorship model: With finite block size, a builder may select up to k bids, omit pending bids, and choose their order before on-chain allocation.A builder-as-user may also inject bids under its own sybil identities.
- Censorship model: The mechanism is assumed anonymous, so allocation and payment depend on reported valuations, budgets, and ordering rather than identity information.This allows a builder-owned identity to substitute for another identity with the same numerical report.
- Impossibility result: No non-trivial anonymous AMM with finite block size can satisfy IR, feasibility, UIC, and builder-as-seller strategy-proofness when censorship is allowed.Non-triviality means some included bid receives strictly positive expected compensation.
- Proof mechanism: Adding many low-ask identities forces at least one identity to have arbitrarily small truthful utility because finite capacity bounds total compensation.For N added identities, some identity has utility at most C/N.
- Proof mechanism: A builder can censor the prescribed block and replace a selected identity with the low-utility builder-owned identity while preserving the same numerical block.Choosing N > 2C/T makes the deviation strictly more attractive, contradicting builder-as-seller incentive compatibility.
A Why Exclude Ineligible Users?
The paper shows that user incentive compatibility is incompatible with Pareto optimality for all users, including ineligible users. The impossibility persists under the weaker local-efficiency requirement, motivating Pareto guarantees only for eligible users.
- Proof construction: The proof constructs a two-user profile with one sell-Y user and one sell-X user, linked by residual AMM input and surplus-disposal variables.Feasibility is represented by yi = yj + p + BY and xj + F(p) = xi + BX.
- Impossibility for all users: Theorem 24 shows that no deterministic finite-reserve AMM can satisfy individual rationality, off-curve feasibility, UIC, and Pareto optimality for all users, including ineligible users.The impossibility already holds with two users, fixed publicly known budgets, and reservation-value misreports only.
- Proof construction: Finite reserves force the sell-Y user to be underfilled, while Pareto optimality forces the sell-X order to execute fully.The argument chooses budgets so that full sell-Y allocation cannot be funded and then rules out underfilling the sell-X user through profitable direct trades with the pool.
- Proof construction: UIC then forces constant compensation across sell-X asks and a large information rent for the sell-Y user, exceeding the AMM’s available surplus and yielding a contradiction.The contradiction uses the forced compensation bound, the low-cost type’s mimicking incentive, and the finite-reserve surplus bound.
- Implication: The impossibility does not rely on full Pareto optimality: UIC is incompatible even with local efficiency, which only rules out profitable direct trades between users and the pool.Thus the paper restricts Pareto guarantees to eligible users, since requiring them for ineligible users is unattainable.
B Necessity of Surplus Redistribution
The paper argues that surplus burning or redistribution is necessary for the desired AMM guarantees. Without burn, exact accounting lets a strategically misreporting user capture the pool’s entire output and violate UIC.
- Implication: Surplus redistribution is therefore presented as more than a technical workaround: it supports UIC, builder strategy-proofness, and Pareto optimality for eligible users.The paper frames redistribution as a mechanism for eliminating MEV while reducing negative externalities associated with builder centralization.
- Impossibility without burn: Theorem 26 shows that no deterministic AMM with zero burn can simultaneously satisfy individual rationality, feasibility, UIC, builder-as-user strategy-proofness, and Pareto optimality for eligible bids.Zero-burn feasibility requires every available token to be paid to users or the builder.
- Proof mechanism: The proof exploits a gap between marginal and average compensation: Pareto optimality selects traders using marginal compensation, while zero burn can force a sole trader to receive the entire pool output.This gap allows an otherwise excluded user to profit by understating its valuation.
- Proof mechanism: Under truthful reports, the cheaper user prevents the second user from trading, so the second user receives zero allocation and zero utility.The argument uses priority, concavity, and the zero-allocation implication yi = 0 ⇒ xi = 0.
- Proof mechanism: After reporting a lower ask, the second user becomes the sole supplier and must sell its full cap; with zero burn and no builder fee, it receives the entire AMM output.Evaluating this deviation at the user’s true valuation produces strictly positive utility, contradicting UIC.
- Scope: The zero-burn impossibility remains even without assuming builder-as-user strategy-proofness when builder fees are prohibited by assumption.In that setting, the zero-builder-fee theorem is unnecessary to the proof.