Splitting an order across wallets earns a trader nothing in this auction, provided the combined budget in the trader's own direction is escrowed before clearing. The guarantee requires two concessions. The paper proves that the budget cap is unavoidable once weak Pareto optimality is required.
Clearing a block together
Zhang, Li, Shi, Zhang, Xia and Han begin with the sandwich attack. A builder in a sequential AMM can see your order and front-run it up to your slippage tolerance. More than 85% of Ethereum blocks come from the top two builders, according to the figure the authors cite from Yang et al. The proposed fix gathers one block's trades into a batch and clears them through an ascending-price auction. Their order within the block ceases to matter.
A buy order, selling Y for X, specifies a value v and budget q. The price clock opens at the pool's spot price p0. At each price, the pool supplies a chord target: the largest cumulative quantity of X whose cost curve lies below a straight line of slope p through the batch's current totals (X, Y). Purchases at the clock price move along that line and therefore leave the target unchanged.
A bidder "clinches" when the remaining supply equals the amount everyone else could still afford at the current price. It then buys continuously as the clock advances. Bidders exit at their value, with every increment charged at or below that value. At the end of the batch, the pool is exactly back on its curve.
The mechanism adapts the clinching auction of Dobzinski, Lavi and Nisan, replacing fixed supply with a target that changes with the state. The authors establish Sybil-proofness for any target meeting five admissibility conditions. Their corollary also resolves the question for the original fixed-supply auction, though tied simultaneous exits are split proportionally rather than handled in the classical fixed order.
A two-sided batch needs an extra step. The minority side fills completely at p0. Its M units of X form the opening stretch of an extended cost curve, each priced at p0. The dominant side faces that curve in the clinching auction; only the remainder settles against the pool. Buyers pay at least p0 per unit. Sellers receive at most p0.
Can a buyer profit from fake sellers?
I find this part the most persuasive. A buyer may submit sell-X wallets of any size because opposite-direction Sybil budgets have no cap. When the buy side remains dominant, fake sellers expand the spot-priced fill by E units. The fill-shift lemma, which limits the benefit from that extra fill, gives U(M+E, Q+p0E) ≤ U(M,Q) + (V−p0)E. The trader must deliver those E units of X at a cost of exactly (V−p0)E. The deviation therefore earns no more than truthful bidding.
If the fake sellers instead change which side dominates, the trader has to deliver at least Qdev/p0 − Q/p0 + η units of X. Here η is the original imbalance. The truthful bid already had a guaranteed payoff of (V−p0)(Q/p0 − η) at spot. The arithmetic closes in either case.
The acknowledgment warrants a pause: "AI proved our conjecture regarding Sybil-robust incentive compatibility." The central proof couples a merged run and a Sybil run through a first-crossing differential inequality. Before a protocol escrows anyone's money on that basis, I would want a second human pass.
Escrow and efficiency pay for the guarantee
The mechanism enforces the cap by requiring the full declared budget in escrow before the batch. Sale proceeds cannot finance another order within that batch. To prevent flash loans from standing in for escrow, the authors separate execution across two blocks: escrow occurs in one, settlement in a later one. We read that two-block arrangement as adding at least one block of latency. It also ties up capital equal to budgets that may never be spent.
Builders must also be unable to censor bids. Citing Shi et al., the authors note that incentive compatibility against Sybils becomes unattainable when censorship is permitted. They depend on consensus-layer inclusion lists such as EIP-7805.
The efficiency concession is explicit. The authors describe their guarantee as a relaxed notion of Pareto optimality. They answer the objection with earlier work by Shi et al., which shows that full Pareto optimality fails whether or not budgets are capped. I accept that argument.
The execution cost still needs saying plainly.
A batch can finish with the pool's marginal price above the values of traders whose orders it filled. If the clock stops along a linear stretch of the curve, the unallocated suffix remains in the pool. Different increments also trade at different clock prices. Traders on the dominant side therefore receive no uniform clearing price.
Declaring 4 and paying 2/49 breaks the mechanism
The impossibility result is my reason for keeping escrow mandatory. Take a constant-product pool normalized to x0 = y0 = 1, giving p0 = 1. User 1 has value 4 and budget 1; User 2 has value 100/49 and budget 2/49. The contradiction requires individual rationality, exact settlement and both clauses of weak Pareto optimality.
Suppose user 1 declares a budget of 4. The mechanism collects exactly 1, its true budget, and allocates F(1) = 1/2 unit of X. Its utility is 4 × 1/2 − 1 = 1. This gives User 1 the batch's entire available surplus, forcing user 2's truthful utility to zero.
User 2 can then declare a budget of 4 as well. Its payment is at most 51/49 − 1 = 2/49, again within its true budget, and its utility is strictly positive. User 1's affordable lie puts a floor of 1 under its truthful utility, leaving user 2 nothing. User 2's affordable lie then strictly outperforms truth.
The paper puts it precisely: "a declared budget can influence priority and allocation even when the mechanism never collects the overstated portion." Each deviation uses a single identity. Fair sequencing or trusted timestamps would therefore leave the unescrowed design exposed.
What would convince a desk
We could not test the mechanism on our data. Such a test requires order-level values and escrowed budgets for each block. Price bars supply neither.
A simulation would merely re-run the theorems. The unresolved question is empirical: how much surplus does the retreat to weak Pareto optimality cost real flow? That includes batches closing above served traders' values and unreleased lump suffixes. The comparison is with Uniswap execution net of sandwich losses, after pricing in two-block latency and locked capital.
We found no simulation or on-chain measurement in the paper. Until someone replays historical order flow using slippage tolerances as values, the honest assessment remains a proof of incentives with execution still an open question.