{"id":"f88ed2ad-d88e-48b2-87fb-f280e3c0be1e","arxiv_id":"2508.16823","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"SPA satisfies two new relaxed incentive-compatibility notions, RAIC and OAIC, that compare worst-case or best-case equilibrium outcomes.","lead":"This paper proposes two relaxed versions of advertiser incentive compatibility for auto-bidding auctions, called RAIC and OAIC, and claims that the second-price auction satisfies both. It offers a way to model advertisers who are pessimistic or optimistic about which equilibrium will be selected after they report their constraints.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The proof of SPA satisfying RAIC/OAIC requires a full characterization of equilibrium outcome sets for every misreport; the abstract provides no evidence for it.","rationale":"The reader's verdict is UNVERDICTED because only the abstract is available and no proof can be checked. My stress test identifies the same core weakness: the definitions of RAIC and OAIC require comparing extreme equilibrium outcomes across report profiles, and the abstract gives no guarantee that those extrema exist, are attained, or satisfy the needed set-wise inequalities. This is a load-bearing concern because if the full proof only establishes a property for a subset of equilibria or under a particular tie-breaking convention, the central claim as stated would not follow. The proposed concrete test is a finite computational enumeration of equilibria in the simplest nontrivial case (two advertisers, uniform bidding), which would at least expose a counterexample if the claimed domination property is false in that setting. Since I have no access to the full proof, I cannot move the verdict beyond unverdictable; the review remains UNCHANGED from the reader's UNVERDICTED assessment.","tokens_in":839,"tokens_out":3324,"duration_ms":45861,"concrete_test":"Obtain the full text and isolate the lemma (or theorem) that, for every report profile, characterizes the set of equilibrium outcomes of the induced SPA auto-bidding game. Independently re-derive this set for a two-advertiser instance with uniform bidding: fix two value reports, enumerate all pure-strategy equilibria of the induced game, and compute the minimum and maximum advertiser payoff across all equilibria. Then change one advertiser's report and repeat. Check whether min_truth >= min_misreport and max_truth >= max_misreport hold for all grid points in a fine discrete value grid. If a counterexample is found, the central claim is false; if none is found, it provides computational support for the characterization.","verdict_should_be":"UNCHANGED","load_bearing_attack":"RAIC and OAIC are defined as inequalities between the least (or most) favorable equilibrium outcomes under truthful and misreported constraints. For such statements to be meaningful, for every report profile the set of SPA auto-bidding equilibrium outcomes must be nonempty and the relevant extrema attained. The central claim therefore rests on an unstated set-wise domination property: for every misreport r', the truthful equilibrium outcome set must be at least as favorable at the specified quantile as the misreport equilibrium outcome set. Merely exhibiting one equilibrium per report, or assuming a fixed tie-breaking rule, would not establish the property because RAIC/OAIC quantify over all equilibria. The abstract gives no details on tie-breaking, information structure, constraint space, or why equilibrium outcomes are bounded. If some misreport induces multiple equilibria with a low worst-case outcome, RAIC could fail even if a carefully selected equilibrium looks good. The two-advertiser uniform-bidding result may impose extra restrictions that do not hold in the general case, but the abstract does not clarify whether the main claim is restricted to that setting.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces two relaxations of Auto-bidding Incentive Compatibility (AIC): Risk-Averse AIC (RAIC) and Optimistic AIC (OAIC), comparing least-favorable or most-favorable equilibrium outcomes under truthful and misreported constraints. The abstract claims that SPA satisfies both RAIC and OAIC, and that this also holds for two advertisers using uniform bidding. The manuscript available for review consists only of the abstract; no model formalism, theorem statements, or proofs are provided. The central claim is therefore presently unverifiable.","tokens_in":1153,"tokens_out":3526,"duration_ms":38968,"significance":"If the claimed results are correct, this is a meaningful contribution: it shows that the negative AIC result for SPA can be overturned under natural refinements of equilibrium selection, and it provides a vocabulary for advertisers with different attitudes toward equilibrium multiplicity. The conceptual distinction between risk-averse and optimistic advertisers is attractive and likely to be useful in mechanism design for auto-bidding. However, the significance is conditional on a full proof; the abstract alone does not establish the set-wise domination properties that the definitions require.","major_comments":[{"comment":"The central claim that SPA satisfies RAIC and OAIC is asserted without proof. Because RAIC/OAIC quantify over all equilibria for every report, the proof must characterize the equilibrium outcome set for each report (or establish a set-wise domination relation). The abstract gives no model (values, constraints, tie-breaking, information structure) and no indication of how this characterization is obtained. This is load-bearing, and the current abstract is insufficient to assess correctness.","section":"Abstract"},{"comment":"Definitions of RAIC/OAIC require nonempty equilibrium outcome sets and attained extrema for every report. The abstract does not state conditions ensuring existence, compactness, or continuity. If some misreport has an empty equilibrium set, the inequality is vacuous; if outcomes are unbounded, the relevant minimum/maximum may not exist. These issues must be addressed for the definitions to be well-posed.","section":"Abstract"},{"comment":"The relationship between the general claim and the two-advertiser uniform-bidding result is unclear. Does the two-advertiser result follow from the general theorem, or is it a separate restricted setting? If uniform bidding imposes extra restrictions, then the abstract's initial claim 'SPA satisfies both RAIC and OAIC' may be overstated. Please clarify the theorem scopes.","section":"Abstract"},{"comment":"The abstract does not demonstrate that the RAIC/OAIC relaxations are non-vacuous. Since AIC is known to fail for SPA, it would be important to exhibit a report profile and an equilibrium outcome where AIC fails but RAIC/OAIC hold. Without such an example, the reader cannot tell whether the result is a substantive finding or an artifact of weakening the definition until it becomes trivial.","section":"Abstract"}],"minor_comments":[{"comment":"The abstract mentions 'ordinal preferences' but does not explain how RAIC/OAIC encode them; a sentence or example would help.","section":"Abstract"},{"comment":"Cite Alimohammadi et al. at first mention rather than just naming them.","section":"Abstract"},{"comment":"The notation RAIC/OAIC should be defined formally with equations in the abstract or introduction; the current verbal definition is ambiguous about tie-breaking quantifiers.","section":"Abstract"}],"recommendation":"uncertain","confidential_remarks":"The manuscript appears to be a theory paper in mechanism design. For this journal, the abstract is not sufficient to evaluate novelty; the full proof is necessary. The lack of full text in the review package prevents a soundness determination."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe one thing to know: this is an abstract-only review, so everything below is about what the abstract claims, not what the paper proves.\n\nWhat's new: RAIC and OAIC are natural relaxations of Alimohammadi et al.'s AIC, replacing the stringent worst-truth vs best-deviation comparison with quantile-style comparisons. Showing SPA satisfies both is a genuine extension, since prior work showed SPA fails AIC. The two-advertiser uniform-bidding result is an additional data point. If the proofs hold, this gives auction designers a more flexible toolkit for reasoning about equilibrium uncertainty in auto-bidding.\n\nThe soft spot is exactly the stress-test note: RAIC/OAIC quantify over all equilibria for each report. To prove the inequalities, the authors need a characterization of the equilibrium outcome sets — or at least a domination argument across sets — for every misreport. The abstract gives no details on tie-breaking, information structure, or the constraint space, so the central claim is unverifiable from the abstract alone. That doesn't mean it's wrong; it means the soundness score is low because there's no evidence, not because there's a flaw.\n\nOne additional thing: the abstract says 'SPA satisfies both' without saying whether that's for the general model or only under uniform bidding. The 'furthermore' sentence suggests the uniform-bidding result is separate, but it's worth clarifying in the final version.\n\nMy recommendation: this deserves a serious referee. The definitions are well-motivated, the result is non-trivial relative to the prior AIC failure, and the paper is within an active research program. A referee should push for the full equilibrium-set characterization and for explicit statements about assumptions. I would not cite this yet myself, since I can't verify the core claim, but I'd want to see the full paper.\n\nBest.","headline":"Plausible and potentially useful relaxation of AIC, but the abstract alone cannot support the claimed SPA results.","tokens_in":1538,"tokens_out":1712,"would_cite":false,"duration_ms":19952,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["91B26"],"pacs":[],"model":"deepseek-v4-flash","headline":"Second-price auctions are incentive-compatible for auto-bidding advertisers under both worst-case and best-case equilibrium selection.","keywords":["auto-bidding","incentive compatibility","second-price auction","equilibrium selection","truthful reporting","advertiser constraints","uniform bidding","risk attitudes"],"falsifier":"Take an auto-bidding instance in the paper's model and solve for all SPA equilibria under some misreport. If the misreport's minimum advertiser utility is higher than the truthful minimum, RAIC fails; if the misreport's maximum is higher than the truthful maximum, OAIC fails. A concrete numerical example of either case would settle the claim.","tokens_in":804,"feed_emoji":"🔨","tokens_out":6272,"duration_ms":75702,"temperature":0.7,"pith_summary":"This paper asks whether auto-bidding advertisers can be trusted to report their true constraints when a second-price auction selects outcomes. It argues that the earlier notion of auto-bidding incentive compatibility was too demanding, because it compared the truthful worst-case outcome against the best-case outcome from lying, and both first- and second-price auctions failed that test. The paper introduces two refined conditions: risk-averse incentive compatibility, where truthful worst-case outcomes are no worse than any misreport's worst-case, and optimistic incentive compatibility, where truthful best-case outcomes are no worse than any misreport's best-case. Its central claim is that the second-price auction satisfies both conditions, and that the same holds for two advertisers using uniform bidding. If true, truthful reporting is a safe recommendation for advertisers with both pessimistic and optimistic attitudes toward equilibrium uncertainty.","feed_headline":"Second-price auctions pass two new auto-bidding truthfulness tests","feed_subtitle":"Truthful reports win under worst-case and best-case equilibrium selection in second-price auto-bidding.","key_machinery":"The mechanism is the comparison of equilibrium-outcome intervals. For each reported constraint, an advertiser faces a range of possible final outcomes, and the paper's incentive conditions evaluate only one end of that range: RAIC compares least favorable outcomes, while OAIC compares most favorable outcomes. The argument carries by showing that, under SPA, the relevant endpoint of the truthful-report interval dominates the corresponding endpoint of every misreport interval. The paper also uses a restricted strategy class, uniform bidding, to obtain the two-advertiser result.","core_discovery":"The paper's central claim is that, in its auto-bidding model, the second-price auction (SPA) is incentive-compatible under both refined definitions. RAIC requires that the advertiser's least favorable equilibrium outcome after truthful reporting is at least as good as the least favorable equilibrium outcome after any misreport; OAIC makes the same comparison for the most favorable outcomes. This is weaker than the prior AIC notion, which compares truthful worst-case outcomes to the best-case outcomes of any deviation and which the paper notes both first- and second-price auctions fail. Under the refined definitions, SPA passes both bars, so truthful constraint reports are weakly preferred re","pith_inferences":["The same endpoint-comparison idea could be tested on first-price auctions and other formats; the paper does not claim the result holds there.","RAIC and OAIC could be used as equilibrium-selection-dependent incentive constraints in mechanism design, letting a designer guarantee truthfulness under a specified selection rule.","A natural testable extension is whether the two-advertiser uniform-bidding result scales to more advertisers or to general bidding strategies; the abstract does not address that."],"forward_implications":["Under SPA, platforms can tell auto-bidding advertisers that truthful constraint reports are weakly optimal regardless of equilibrium-selection attitude.","The earlier conclusion that SPA is not auto-bidding incentive-compatible no longer applies under either relaxed comparison.","Advertisers with different ordinal preferences over constraint types can be modeled by choosing which equilibrium-endpoint comparison applies.","For two advertisers, even the restricted uniform-bidding strategy class preserves both guarantees."],"supporting_citations":[],"fun_headline_variants":["SPA passes two new truthfulness tests in auto-bidding","Second-price auction meets new auto-bidding incentives","New definitions show SPA is incentive-compatible","Auto-bidding: second-price auction clears risk and optimism bars","SPA truthfulness holds under risk-averse and optimistic bidders"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The result rests on the paper's characterization of the possible SPA equilibrium outcomes: if that characterization misses a misreport whose worst or best equilibrium outcome beats every truthful outcome, RAIC or OAIC fails.","fun_headline_variants_meta":{"raw":{"variants":["SPA passes two new truthfulness tests in auto-bidding","Second-price auction meets new auto-bidding incentives","New definitions show SPA is incentive-compatible","Auto-bidding: second-price auction clears risk and optimism bars","SPA truthfulness holds under risk-averse and optimistic bidders"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000167,"raw_usage":{"total_tokens":1143,"prompt_tokens":842,"completion_tokens":301,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":586,"completion_tokens_details":{"reasoning_tokens":219}},"tokens_in":586,"tokens_out":301,"duration_ms":4052,"temperature":1.0,"reasoning_tokens":219,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T17:07:05.132499+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take an auto-bidding instance in the paper's model and solve for all SPA equilibria under some misreport. If the misreport's minimum advertiser utility is higher than the truthful minimum, RAIC fails; if the misreport's maximum is higher than the truthful maximum, OAIC fails. A concrete numerical example of either case would settle the claim.","supporting_citations":[],"review_version":1}