How much market value do agents leave on the table, and how much is provably recoverable?

Same 5-agent market as the leaderboard above, one difference in who fills the seats. Single-seat is the model in one seat against a four-agent frozen panel; that is the leaderboard score. Population fills all five seats with copies of the same model. The test: does a single-seat edge survive when every counterparty is a copy of itself? Four models were run this way in the official AER, but three are withdrawn pending re-measurement (see below), leaving the panel model as the one usable row; for it, population and single-seat coincide (+.112 vs +.111), a built-in self-consistency check, since its frozen panel is the same model at the same temperature.

This comparison is on hold. Three of the four population rows (deepseek-v4-flash, minimax-m3 and glm-4.7-flash) were measured before we found the empty-response defect (see the board note above), and so were their single-seat scores, so both sides of the solo-vs-population comparison are contaminated for exactly those models. Rather than restate numbers we cannot stand behind, we withdraw the rows until the population runs are re-executed. The panel model is unaffected (it runs on a different provider path with no empty turns) and its check still holds: its pooled population AER (+.112) tracks its single-seat score (+.111), which is the self-consistency result the frozen-panel design predicts. The question itself is untouched by the defect (same seats, same worlds, same scoring), so the claim we keep is the weak one: population scores are not a mechanical function of solo scores, and a solo leaderboard is not yet evidence about market-level welfare. The quantitative version returns with the re-run. The scale-collapse and under-trading ceiling reported under Findings come from legacy self-play (population welfare-ratio), a separate measurement, not on this board.

Capture: the second axis, and why AER cannot be it. AER is a sum over agents. Surplus moved from one seat to another leaves it unchanged, so it cannot express who captured value or who was protected from a bad settlement, the two questions a principal deploying an agent actually asks. This is a property of the measure, not a defect in it, and it is demonstrated rather than argued. Three measurements: (1) over 100 exactly-evaluated worlds AER ranks an offer giving the responder 45% of the joint gain above one giving it 71%, because the ordering tracks trade volume; (2) an intervention that cut settlements leaving an agent worse off from 7.3% to 1.8% (paired CI [−.090, −.021]) moved AER by −.018 with an interval spanning zero; (3) on the bargaining track below, nearly every model closes nearly every deal, so AER-style clearing barely separates them, while capture spans .06 to .16 against a waiting rule that scores .19.

How capture is computed. A buyer (the model under test) bargains over price against a scripted seller that bargains back: it concedes faster when the buyer moves toward it and slower when the buyer stalls, may end the negotiation outright if an offer is far beneath its ask, and holds a private reservation above its cost that declines as rounds run out. The buyer knows its own maximum willingness to pay and the public list price, never the seller’s cost. The metric is SE+ = buyer surplus / ZOPA width, where the zone of possible agreement is WTP − cost, both known exactly to the scorer and hidden from the agent, so the denominator is exact with no bargaining-solution or Bayesian fixed point to approximate. That is why capture is measured here and not in the five-agent arena: with five seats, “you could have captured everything” is unreachable by anyone, and share-of-realised-joint-gain diverges when a counterparty loses (measured at 3.7 on one case). SE+ needs no discrimination correction because closing is a precondition for scoring: a model that never deals scores 0, and one that lowballs into no-deal scores 0. Anchors on the same worlds: accepting the opening ask scores −.565; a one-line stubborn rule that counters every round at 80% of whatever is currently asked and never raises its own offer scores .188; the best fixed schedule found by grid search scores .468; the per-world hindsight ceiling is .613; paying exactly the seller’s cost is 1.0. The stubborn rule is a bargaining policy, not a passive one: it makes three counter-offers and the seller accepts its price in 21 of 30 worlds. It is the right yardstick precisely because it is so simple, and because the gap above it (.468 versus .188) shows that skilled bargaining is worth two and a half times what stubbornness alone earns. A model below .188 is therefore not being punished for negotiating; it is negotiating worse than refusing to move.

Robustness, and what it rules out. 629 of 630 episodes, 7 models × 30 seeds × three arms. Rank agreement between public development seeds and a private held-out set nobody could tune against is Spearman +.86, and gemini-3.5-flash leads all three arms. Agreement with the second archetype is weaker (+.46), which is the reason the second archetype exists: one scripted concession family is one counterparty model. That archetype opens far above willingness to pay and concedes fast, against a standard seller that opens modestly and concedes slowly, so the pair differs on both axes rather than being a relabelling. Two candidates were screened out first: a stubborn seller collapsed the gap between naive and informed play to .031, and a late-concession schedule revealed the seller’s cost outright. The generator itself was rebuilt for the same reason: its first form was algebraically invertible, recovering the private cost in 200 of 200 worlds, which would have measured whether a model spotted an identity rather than whether it could bargain.

The result is not an artifact of the seller or the instructions. Two objections have to be answered before “every model loses to a waiting rule” means anything. First, the models might be losing to an environment that is simply harsh. They are not: measured on their own transcripts, 67% of deals settled above the price the seller was itself asking by the final round (mean overpayment $8.20), and replaying each episode with the buyer repeating its own first offer instead of climbing gains +.100 SE+, better in 142 of 202 matched scenarios. Both comparisons hold the world, the seller and the rules fixed, so they isolate the choice. Second, the buyer prompt discloses that the seller may walk away and that its concession responds to movement, which could plausibly be instructing the bidding-up. So the disclosure was made switchable and removed: across 3 models and 30 shared seeds the paired change in SE+ is −.003 with a 95% interval of [−.029, +.022], and the self-bidding rate moves from 89% to 84%. A null. What does remain design-relative is the level: a more generous reservation or a faster concession schedule lifts every number, and four rounds bounds how much patience can pay. The ordering, the self-bidding rate and the two counterfactuals above are within-environment comparisons and do not depend on those choices.

What the capture column does and does not license. It licenses this: against this seller, every model tested bargains worse than a one-line rule that never raises its own offer, and does so by conceding toward the counterparty as the counterparty concedes toward it. The stubborn rule’s absolute offers fall in 30 of 30 worlds; the models’ rise in 166 of 202. Bargaining itself pays here, and pays well: the best schedule earns .468 against the rule’s .188. The deficit is directional, not a case against negotiating. It does not license reading .16 as a constant for gemini-3.5-flash: that number is relative to this seller’s parameters. It does not license any capture claim about the multi-agent arena, which needs a per-pair attainable frontier that is not built. Capture is reported beside AER and never averaged into it, because a composite would re-hide exactly what the second axis exists to expose, and the two agree only weakly (Spearman .18). Counterparty surplus is shown alongside because SE+ = 1.0 means the seller received nothing, which is the correct answer for a principal-agent measure and the wrong thing for a benchmark to celebrate silently.

What is being measured, and what is only the control. The quantity is private value capture: each side is given a private value it alone knows, and the score is the share of the available gains it secures for itself, against a fixed reference bargainer that concedes on a schedule and is never adjusted between runs. That is the number an agent’s principal cares about, and it is the one AER cannot express, being a sum over both sides. Across the field it is .217, and only minimax-m3 separates from the rest: .309 [.265, .354] against five models spanning .147 to .255 with mutually overlapping intervals, so ranks below the leader are unresolved. Symmetry is the experimental control, not the finding. Models play a round-robin: every pairing, four cells per scenario crossing which side each holds with who opens, so both cancel by construction rather than by argument. Each episode scores both participants, since the two shares sum to one; an earlier version recorded only one side and would have published a leaderboard silently omitting gpt-5.6-luna, with per-model sample sizes running from 120 to 599. The metric is the split among closed deals, with deal rate reported beside it and never folded in: a variance decomposition put 57.2% of the previous composite on deal-versus-no-deal, which is what AER already measures, and only 9.1% on model identity. Conditioned on a deal, model identity rises to 13.8% and the side held falls to 0.0%. The round-robin exists to establish that the capture number is not an artifact of which chair a model was put in: there the field divides gains near evenly (.34 to .62), so the low capture against the reference is a property of the bargaining rather than of the seating. The reference policy takes no model calls, which is what makes an absolute reading affordable at all.

The gate, and the two checks in it that could not fail. A run reports nothing unless it passes: cell balance (every model in all four cells, near-equal counts), deal rate inside .40 to .95, unreadable-turn and reservation-veto rates under 5%, split-half rank stability above .70, and position effects bounded at .25. This run passed at balance 150/150/150/150 per model, deal rate .72, unparsed 3.7%, veto 3.3%, stability +.94. Two earlier members of that check set were removed for being unfalsifiable. Self-play balanced capture is an accounting identity: the four cells are two episodes counted from both sides, so it reads .5000 for every policy including deliberately lopsided ones. And split-half stability returned 1.00 whenever fewer than three models had data, so partial runs sailed through; it now blocks as "not evaluable". The gate also originally blocked on the size of the position effects rather than the balance of the design, which is the wrong test: chess counterbalances colour rather than abolishing white’s advantage, and effects of +.062 and +.093 that cancel exactly contribute 1.1% and 2.5% of variance against model identity’s 8.1%.

The seat was worth more than the model, and we did not notice until we looked. Every capture number this axis produced before 5 August 2026 seated the model under test on the buying side. Asked whether that side was harder, we mirrored the two seats word for word and swapped the models into each. Swapping sides is worth +.528 of the bargaining range [+.431, +.627]; the prompt wording, which was the suspect we started with, was worth +.043. The same gemini-2.5-flash kept .006 buying and .661 selling; minimax-m3 kept .066 and .829. Four structural features caused it, none of them deliberate: one side proposed and the other disposed, so the responder held the last word every round; the opening number was the seller’s published list price, for which there is no buyer equivalent; the seller’s counter reset the reference each round; and a known four-round deadline made whoever answered last a take-it-or-leave-it player. The prompt asymmetries we had already fixed were a twelfth of the effect of the ones we had not seen.

What survives, and what does not. The claim that models keep almost none of the bargaining range does not survive as a statement about bargaining: it is substantially a statement about which seat they were given. What does survive is every comparison made within that seat, because the reference policies were played there too. A one-line rule that counters at 80% and never raises its own offer kept 22% of the range in the same disadvantaged seat, and no model kept as much. The seat is hard, not hopeless, and losing to a trivial rule playing your own side is a fair verdict. The pooled 99.6% counterparty share is withdrawn as a headline for the same reason the earlier patience-ranked column was: not wrong arithmetic, but a number that answers a different question than the one it appeared to answer.

The rebuilt protocol, and the check it had to pass first. Bargaining now alternates who proposes; neither side gets a published anchor, so each knows only its own value; the negotiation ends at a random moment rather than a countable deadline, because a known deadline is not merely unfair but solvable by backward induction, which would measure whether a model can count rounds; and every world is played twice with the seats swapped, so residual advantage cancels the way playing both colours cancels it in chess. Acceptance criteria were written down before the check was run and measured offline with scripted policies at no cost: the residual seat gap between identical policies is 0.000 against +.528 for the design it replaces, counterbalanced capture is .500 to four decimal places, and bargaining skill still separates monotonically, so fairness was not bought by making the case degenerate. A raw first-proposer effect of −.069 remains and is cancelled rather than hidden, with a test asserting it is still present: if it silently vanished, the reference policy has most likely gone degenerate, which it did once already during this work.

Why the published opponent is a live model, not a script. The first version of this axis bargained against a scripted seller with five parameters (concession rate, two reactivity terms, a walkaway threshold, a reservation share) and we chose them by grid search, on the same development seeds the scores are reported on, to maximise the gap between good and bad play. That is a researcher degree of freedom: a result measured against it is partly a result about our choices. The remedy in this literature is more than one counterpart family, so we built a second and then published the better of the two. The A2Frozen seat is what the landing page reports: the seller is a live model, pinned at temperature 0, given a private cost and told to get the best price it can. That world carries no concession parameters at all, only a list price, a buyer value and a seller cost, because a model is not told how to bargain. SE+’s denominator is unaffected, since we still assign the cost. Two things the engine still enforces rather than requests: an accept below the seller’s cost is vetoed, and an unreadable seller turn becomes a hold rather than an accept. Across 418 episodes the veto fired zero times and no seller turn was unreadable, so the guard was present and never needed.

What the scripted opponent said, and why it is not the published number. Both were measured on the same seven models. The headline holds under each, and is stronger against the live opponent: every model still lands below the stubborn rule, by more (a gap of roughly .20–.26 against a live agent, versus .03–.13 against the script), self-bidding rises to 94% of multi-round episodes, the counterparty ends with 99.6% of the range, and deal rates fall from .93 to .64, so the models lose the deal as well as the surplus. What did not survive is the ordering below first place: rank correlation between the two counterparts is only .32, and minimax-m3 falls from second to last. Two separate live sellers (gemini-2.5-flash and kimi-k2) were run so that this could be attributed: they agree with each other at .86, so the instability is scripted-versus-live, not one model’s quirk. Own-family pairing is negligible: paired within buyer, a model scores +.003 against a seller from its own family, and the pooled figure of +.012 is a composition artifact of the three buyers that have such a cell. Consequently the landing page reports the live opponent alone, and treats per-model ranks below the leader as unresolved. The scripted numbers are kept here rather than deleted, because the disagreement between the two is itself the reason to distrust any single-opponent ranking, including this one.

Withdrawn: the capture numbers published on 4 August 2026. The first version of this column (deepseek-v4-flash .73, gpt-5.6-luna .64, gemini-3.5-flash .62, glm-4.7-flash .55, minimax-m3 .43, kimi-k2 .41, gemini-2.5-flash .39) was measured against a seller that read the buyer’s offers only to check whether they cleared its ask. Its concession path was a function of the round number alone, so offers of $1 and $40 produced identical outcomes, lowballing carried no risk, and the final round accepted anything above cost. Waiting therefore scored .729 and beat every counter-offer policy, and the column ranked models by how long they waited (patience explained it at Spearman +.82). Those numbers are withdrawn rather than quietly amended. The rebuilt ordering anticorrelates with them at Spearman −.25: deepseek led the old column and places fifth here; gemini-3.5-flash was third and now leads every arm.

Terms & provenance for the landing page. The landing page translates several terms of art that resolve here. (1) market-ext: the market-extension probes it cites (procurement bundling, private-value auction, cyclic clearing, coupled B2B award, hidden-reservation pricing) were scripted-mode runs with gpt-5.5 as the model under test (construction cases n=30, hidden-reservation pricing n=20), a separate track from the A2A leaderboard; their headline contrast is 1.00 on the visible variant vs −0.29 once the reservation is hidden. (2) The market-mode ceilings “≤ .36” and “≈ .15” come from the 2026-06-30 self-play parameter sweeps (gemini-2.5-flash populations, welfare-ratio, mean over 3 seeds): .36 is the best population ceiling across the five single-knob friction settings (population size, temperature, visibility, ledger row limit, search cost); .15 is the ceiling of the visibility knob specifically: legacy welfare-ratio, not AER. (3) The “admission screen” is the regret-normalized criterion from the case-oracle spec: a case is admitted iff an informed-but-naive policy (correct posterior beliefs, a simple non-optimizing rule) leaves normalized regret ≥ τ ≈ 0.3 against the Bayes-achievable frontier, so admission requires a hard control problem, not just hidden information; visible-construction and cheap-talk-style cases are rejected, and the screen runs independently of any model provider. (4) The baseline agents (greedy floor, random, no-op) are defined exactly on the methods page; the frozen panel decodes at temperature 0, as stated at the top of this page. (5) Agents are scored with reasoning disallowed in the public channel. The arena’s response prompt ends “no scratchpad, no private calculations, and no reasoning before PUBLIC ACTION”, because anything an agent writes there is read by its counterparties, and the private values it would reason about are exactly what the hidden-information cases withhold. That is a deliberate choice with a measured price on both sides. Every number on this site is the reasoning-disallowed arm.

What that condition costs, measured. Asked to accept or refuse the same settlements, the same models discriminate almost perfectly when allowed to compute (accepting 97.6% of the trades that help them and 0.0% of those that hurt) and not at all inside the negotiation, where they accept harmful settlements slightly more often than beneficial ones. The capability is present; the channel suppresses it. Giving agents a private scratchpad that is stripped before anyone else sees it cuts settlements that leave an agent worse off from 7.3% to 1.8% in a live market (95% CI on the paired difference [−.090, −.021]), and moves the score on this page by −.018, an interval spanning zero. Forbidding the reasoning buys a 0% rate of leaked private values, against 90% when it is allowed unshielded. So the condition is defensible and it is not free: it costs real counterparty discipline that a welfare score cannot see. Numbers here are correct for the condition stated; they are one arm of a two-arm design, and the fuller picture belongs beside them rather than behind them.