A dark pool's welfare lead is no routing instruction. Aldridge gets that ranking from a queueing model, while a desk pays attention to realized fills and slippage. The survey is strongest when it shows how venue rules determine waiting, information exposure and priority before a price prints.
The paper follows market design from trading floors and high-frequency trading through lit, dark and batch venues, OTC and RFQ markets, AMMs and extractable value, algorithmic collusion, and the new agent protocol stack. Its recurring question is how to allocate scarce goods fairly and efficiently when participants keep some of their preferences and information private. Aldridge argues that allocation is the missing layer for AI agents.
In this account, each redesign runs into the same small set of impossibility theorems. Myerson and Satterthwaite's result says a bilateral mechanism cannot simultaneously be efficient, incentive-compatible, individually rational and budget-balanced. Venues choose which property to give up. Aldridge traces the binding constraint from trader rationality on the floor to speed under HFT, ordering control on blockchains and the dimensionality of AI-agent reports. Her summary is sharp: "Impossibility results persist; only their cost moves."
The survey contains no original trading data. Its own quantitative findings come from three companion pieces by the author; figures from other studies remain those studies' figures. One piece models venue welfare with a queue and calibrates it by simulation. Another is a crypto microstructure review prepared for the Federal Reserve Bank of New York. The third tests agent matching on simulated markets in a working paper. Aldridge discloses an affiliation with AbleBlox, developer of the digital dark pool design discussed in the survey.
Why does the dark pool win?
In the venue model, every trader has the same utility formula: side times (valuation minus price), minus waiting cost times wait, minus a fixed cost K. Venues differ only in what traders see and how orders are served. A lit exchange displays the book and uses first-come-first-served priority. A dark pool hides the book but keeps that queue discipline. A batch auction gathers orders for an interval T, then serves them in random order.
The welfare ordering is a theorem within that model. Simulation puts a size on it, under the paper's label "Simulated aggregate welfare." At the baseline (20,000 traders, arrival rate 5, adverse-selection parameter 2, T = 1), welfare is 0.2819 dark, 0.2410 lit and 0.1589 batch. Dark exceeds lit by 17%; lit exceeds batch by 52%. Participation is 46.1%, 43.6% and 39.9%, respectively. Displaying the book invites traders to play for queue position. In the dark, urgent traders can still cross the spread. A batch holds even urgent traders for T/2 on average, while pro-rata rationing excludes marginal traders.
Aldridge presents the result as a refinement of the Budish et al. case for batch auctions: a batch still ends the speed race. The theorem's scope is explicit. It requires arrival rates within a bounded range, bounded adverse selection and a dark reporting delay below T/2. The full ordering holds almost everywhere on a 20 by 20 grid of arrival rates and valuation dispersions. Only thin markets, with an arrival rate below about 2.5, break it; dark still beats lit there.
My objection is to what welfare counts. Execution prices cancel in the model as transfers between buyers and sellers. Aldridge addresses the consequence: traders who expect poor prices at the margin may leave, and she links that participation effect to Zhu's (2014) work on whether dark pools harm price discovery. A regulator should count their exit. A desk still experiences the transfer as slippage.
The survey's periodic-auction evidence shows why that distinction matters. Per the European Securities and Markets Authority (ESMA), 99.9% of orders were pegged to prices set elsewhere, and about 80% crossed at the continuous market's midpoint. Aldridge says those venues "do not perform price discovery; they consume it." Her model specifies no midpoint cross. Yet many dark pools do cross at a lit midpoint and consume prices in the same way; we did not find that cost charged in the welfare calculation. A real-venue participation study reproducing the 2.5 percentage-point gap (46.1% dark vs 43.6% lit) would move me.
Ethereum already batches transactions
The on-chain section has the clearest lesson for traders. Proof-of-stake Ethereum makes a block every 12 seconds. A block builder sees pending transactions in a public mempool and chooses their order. Trades then fill one after another along an AMM curve. There is no uniform clearing price: order determines price. The builder can also place its own trades after seeing the flow.
Aldridge's sandwich example puts prices on that power. The builder buys, moving the pool from 100 to 101. The user's buy fills from 101 to 103, after which the builder sells back to 102. In our view, the batch interval offers no protection against this sequence. Several of the survey's more effective remedies use batch auctions with uniform pricing. A privately filled signed intent also stays out of the public mempool. Bachu et al. (2024) find that order-flow auctions on two major platforms, where solvers compete to fill a signed intent, improved prices by about 4 to 5 basis points over AMM execution. Better access to liquidity for larger trades drove most of that gain. We examined how much a private mempool can leak before a sandwich becomes guaranteed in an earlier review.
The survey argues that control of the queue captures the rent. Our reading puts more weight on ordering control and price uniformity on-chain, and less on interval length. Aldridge does not make that claim. In her discussion of the speed era, interval length carries a real cost that is U-shaped in the interval.
Spectral matching, and the checks it fails
The agent sections turn to scarce goods. AI agents have open protocols for tools (MCP), payment (x402) and identity (ERC-8004), but those protocols leave allocation undecided when agents compete for the same resource. Aldridge proposes spectral feature matching to fill that gap.
An agent reports a short vector of feature weights instead of a full ranking. Its utility is the inner product of its true weights and the product's features, an assumption that rules out complementarities; the report can differ from those true weights. The mechanism projects products and unit-normalized reports onto the leading singular vector of the product-feature matrix, then sorts them. It checks feasibility before allocating: agents with a positive score must number exactly as many as the units above the mean product score. A separate margin check requires the minimum projected gain to exceed four times a projection-error bound. Fairness is measured by Nash social welfare, the product of each agent's gain over random assignment.
The checks usually give unwelcome answers. With only mainstream shoppers (Scenario A), 10 agents score positive for 6 units above the mean, so the mechanism returns Fail. Add four contrarians (Scenario B), and feasibility passes at 6 = 6. Total utility reaches 99.1% of the utilitarian optimum (1,467.6 versus 1,480.8). Yet the margin check fails by three orders of magnitude: 0.26 against 140.8. The warning is borne out by clipped Nash welfare of about 0.27% of the brute-force optimum. A search through 200,000 alternative reports found a misreport worth 33.6 to the harmed agent. Aldridge explicitly says the mechanism is not strategy-proof.
Across 100 random markets, feasibility passed 22 times. The share of agents worse off than under random assignment dropped from 50.3% to 15.6%. Mean log clipped Nash welfare was 17.37, statistically indistinguishable from serial dictatorship's 17.95; serial dictatorship uses true, unprojected utilities. Aldridge's deployment rule sends failed checks to exact search. For a ten-unit drop, that took 16.5 seconds over 10! ≈ 3.6 million assignments. Feasibility failed in 78 of the 100 markets, leaving brute force to handle most rounds. The paper considers that affordable for small, high-stakes rounds, though the cost grows factorially with drop size. Cheap elicitation is the projection's contribution.
The venue ranking still needs fills
We could not test the venue claims on our data. We have minute and daily bars, while the ranking depends on queue position, venue-specific fill rates and dark-print reporting delays. Testing the on-chain claims would require mempool and builder-level block data we do not have.
The survey's venue ranking should remain a hypothesis until realized fills are measured.