{"id":"c9d2df26-81c6-4c0b-b7ad-751fcf194272","arxiv_id":"2608.09409","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":8.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"In a no-transfer project approval problem with two-sided private information, the principal-optimal mechanism is privacy preserving: it never elicits the agent's benefit, and amounts to disclosed cost information plus delegation.","lead":"A principal who must approve a project can get the best possible outcome without ever asking the agent to report his private benefit. The optimal design either decides alone or gives the agent free information about costs and full decision rights, with disclosure doing the work of money.","discovery_kind":"first_principles","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Abstract overclaims no-report optimality: the Bayesian results hold only under single-crossing and monotone-partitional conditions, and no general theorem covers the case where the upper feasibility constraint binds.","rationale":"The reader's strongest_claim correctly identifies the abstract overclaim, and the reader's verdict of CONDITIONAL is appropriate. However, the reader's weakest_assumption (independence of s and t) is not the most load-bearing concern; independence is a clearly stated modeling assumption that limits scope but does not threaten the internal validity of the paper's conditional results. The more pressing issue is that the central claim in the abstract—that the principal-optimal mechanism never requires the agent to report—is not established by the theorems for the general Bayesian IC problem. Theorem 1 covers the ex-post benchmark; Corollaries 1 and 2 cover specific parametric conditions; and Proposition 5/Theorem 2 solve a relaxed problem without verifying the upper feasibility constraint. Appendix G shows that non-delegation mechanisms exist among Bayesian IC mechanisms, and nothing rules out their optimality. Thus the abstract's unconditional statement is unsupported, but the underlying conditional theorems appear carefully proved and constitute a substantial contribution. The appropriate verdict remains CONDITIONAL, requiring the authors to either correct the abstract or prove a general theorem. Since my assessment agrees with the reader's verdict, I set verdict_should_be to UNCHANGED.","tokens_in":37603,"tokens_out":8781,"duration_ms":91172,"concrete_test":"Run a numerical search over a parametric family of densities f (e.g., mixtures of two truncated normals with peaks at t=0.2 and t=0.8, varying the mixture weight and variance) with g uniform and α=0.5. For each instance, solve the full problem (Auct′) with the upper constraint in (Feas′) imposed by discretizing [0,1] into N=1000 grid points and solving the resulting linear program for X and S. Check whether the optimal X satisfies the upper constraint with strict slack for all t and whether X(t)=G(s̄(t)) for a nondecreasing s̄(t) (i.e., implementable by capped delegation with interval censorship). If any instance yields an optimal X for which the upper constraint binds on a positive-measure set, then the implementing interval mechanism must have a(t)>0, requiring the agent to report t, which refutes the abstract's unconditional claim.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The abstract states unconditionally that the principal-optimal mechanism does not require the agent to report. The formal results support this only conditionally. Theorem 1 proves it for ex-post incentive compatibility. For Bayesian incentive compatibility, Corollary 1 requires V to be single-crossing at t0 and convex on [0,t0]; Corollary 2 requires V single-crossing at t0, non-increasing on [0,t0], and the existence of a monotone partitional solution H to the persuasion problem (22). Proposition 5 and Theorem 2 solve the relaxed problem (R) but do not show that the relaxed optimum satisfies the upper feasibility constraint in (Feas′), nor that the resulting mechanism is a capped delegation mechanism. Appendix G constructs a Bayesian IC mechanism that is not implementable by any disclosure-delegation scheme; nothing in the paper rules out that this or a similar mechanism is optimal for some f,g,α. Consequently, the abstract's first sentence is not proved: there is no general theorem establishing that an optimal Bayesian mechanism can always be chosen to be a capped delegation mechanism with interval censorship. The independence assumption (Section 2) is a separate scope restriction and is clearly stated, but the gap between the unconditional abstract and the conditional theorems is the central load-bearing issue.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies a no-transfer principal-agent problem in which the principal privately knows cost, the agent privately knows benefit, and the agent is biased toward implementation. The principal commits to a mechanism before learning her type. The authors characterize ex-post incentive-compatible mechanisms, then reduce the Bayesian incentive-compatible problem to a one-sided auction-design problem with a novel feasibility constraint on the payment rule. They prove strong duality for a relaxed version of the problem, connect the dual to Bayesian persuasion, and show under conditions on the benefit distribution that an optimal mechanism is a capped delegation mechanism, possibly with interval censorship, which does not elicit the agent's report. A numerical example illustrates how the Bayesian-optimal mechanism can differ from the ex-post optimal one. The abstract, however, states the no-report conclusion without the conditions that the formal theorems require.","tokens_in":37831,"tokens_out":10444,"duration_ms":107476,"significance":"If the conditional results hold, this is a substantial contribution to mechanism design without transfers. The Myersonian reduction in Section 4.1, the feasibility characterization in Lemma 4, and the strong-duality results in Theorem 2 and Proposition 5 are elegant and appear correct; Proposition 2 is a broadly applicable structural result. The paper is self-contained: all main claims have detailed appendix proofs, and no parameter is fitted to data. The numerical example in Example 5 cleanly illustrates the distinction between the ex-post and Bayesian optimal mechanisms. The main caveat is that the headline claim in the abstract is currently stronger than the theorems; this needs to be corrected, and one proof step in Corollary 2 should be made explicit.","major_comments":[{"comment":"The abstract states unconditionally that the principal-optimal mechanism does not require the agent to report. This is proved for the ex-post IC benchmark in Theorem 1, but for the Bayesian problem it is proved only under the hypotheses of Corollary 1 (V single-crossing at t0 and convex on [0,t0]) or Corollary 2 (V single-crossing and non-increasing on [0,t0], plus existence of a monotone partitional solution to the persuasion problem (22)). Theorem 2 and Proposition 5 solve the relaxed problem (R), which drops the upper feasibility constraint of (Feas'), and they do not show that a relaxed optimum is feasible for (Auct') for arbitrary f, g, and alpha. The unqualified sentence in the abstract is therefore not a theorem of the paper; please either prove a general version or restrict the abstract and introduction to the conditional statement.","section":"Abstract; Section 4.3; Theorem 2; Proposition 5; Corollaries 1-2"},{"comment":"After showing that Xhat = Hhat(min{t0,t}) solves the relaxed problem (R), the proof of Corollary 2 asserts that Xhat solves (Auct') and then constructs a capped delegation mechanism with interval censorship that 'implements' Xhat. Because (Auct') includes the upper bound in (Feas'), this assertion requires verifying that the constructed mechanism indeed has moments (Xhat, Shat) with Shat satisfying (Feas). The verification is not carried out in the proof; in particular, the displayed construction must show that the censorship thresholds satisfy m_i = E[alpha s | s in (s_i, \\bar s_i]] and that the cap c equals G^{-1}(Xhat(t0)). Please add the calculation or spell out the reference to Example 4.","section":"Appendix R, Corollary 2"}],"minor_comments":[{"comment":"The introduction says 'any mechanism -- incentive compatible or not -- is interim-equivalent to an interval mechanism.' Proposition 2 proves this for moments, but Appendix K notes that the constructed interval mechanism is not ex-post IC even when the original mechanism is. Please add the qualifier 'interim-equivalent, in the sense of equal moments' and note that ex-post IC is not preserved.","section":"Introduction, p. 2; Proposition 2; Appendix K"},{"comment":"The variables m, \\bar m, t, \\bar t, t0, \\bar s, and c are used in Figure 3 and in Example 4 before all of them are defined in the text; please define them in the caption or immediately before the figure.","section":"Figure 3 and Example 4"},{"comment":"Corollary 2 relies on the existence of a monotone partitional solution to the persuasion problem, but Remark 10 only refers the reader to Dworczak and Martini (2019). Please state a precise sufficient condition or a self-contained existence result so that the scope of Corollary 2 is clear.","section":"Remark 10"}],"recommendation":"major_revision","confidential_remarks":"The paper is a solid contribution and should not be rejected. The main revision is to align the abstract and introduction with the conditional theorems and to complete the verification in Corollary 2. I do not see a circularity or a fitted-parameter problem; the independence assumption in Section 2 is explicit and is a genuine scope restriction."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Readable and worth refereeing. The genuinely new piece is the transposition of a no-transfer bilateral private information problem into a one-sided auction with a new interim feasibility constraint, and the resulting characterization: payments are feasible iff they satisfy a budget restriction and weak majorization. The interval-mechanism equivalence (Prop 2) is broader and clean; the duality results (Thm 2, Prop 5) connect to Bayesian persuasion in a way that is not just analogy. The proofs are detailed, self-contained, and checkable; no fitted parameters or hidden assumptions beyond the clearly stated independence of s and t.\n\nThat said, the abstract overclaims. The unconditional statement that the principal-optimal mechanism does not require the agent to report is not proved. Theorem 1 gives it for ex-post IC. For Bayesian IC, Corollary 1 needs V single-crossing at t0 and convex on [0,t0]; Corollary 2 needs V single-crossing at t0, non-increasing on [0,t0], plus existence of a monotone partitional solution to the persuasion problem. Proposition 5 and Theorem 2 solve the relaxed problem; nothing shows the relaxed optimum satisfies the upper feasibility constraint in (Feas') or is implementable as capped delegation. Appendix G even constructs a BIC mechanism not implementable by any disclose-delegate scheme; the paper does not rule out such a mechanism being optimal. So the headline is a genuine gap, not a stylistic quibble.\n\nIndependence of s and t is load-bearing and explicit; that is fine, but it means the scope is narrower than the abstract's first sentence suggests.\n\nThe conditional results are likely correct and are a real contribution. Mechanism design theorists working on delegation, persuasion, or no-transfer screening will get value. The paper deserves a serious referee. I would recommend major revision: either add a general theorem covering the upper-binding case or rewrite the abstract and introduction to state the conditions. With that fix, I would cite it.","headline":"Strong conditional results on no-transfer mechanism design, but the abstract's unconditional no-report claim outruns the theorems.","tokens_in":38307,"tokens_out":2915,"would_cite":true,"duration_ms":30806,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["91B26","91B03"],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper shows that when a principal and an agent both hold private information and monetary transfers are impossible, the principal's optimal mechanism never requires the agent to report his benefit: she either ignores him or discloses…","keywords":["mechanism design","no-transfer contracting","delegation","Bayesian persuasion","interim equivalence","interval mechanisms","information disclosure","privacy-preserving mechanisms"],"falsifier":"Take the paper's own Example 5 densities but perturb them so that $V$ crosses zero twice instead of once, and solve the relaxed problem (R) exactly; the paper's construction predicts the optimum is still attained by $X(t)=H(\\min\\{t_0,t\\})$ for a single $t_0$, while a true optimum that requires eliciting the agent's type would refute the abstract's broad claim.","tokens_in":37411,"feed_emoji":"🤝","tokens_out":13928,"duration_ms":130551,"temperature":0.7,"pith_summary":"The paper asks what a principal can achieve when she commits to a mechanism without monetary transfers, with two-sided private information: she knows the cost of a project, the agent knows its benefit, and the agent does not fully internalize the cost. The central claim is that the principal-optimal mechanism never needs the agent to report his benefit: it either rejects the project outright or discloses the cost (fully or by interval) and hands the decision to the agent. This makes the optimal mechanism privacy-preserving, and it works because disclosure shapes the agent's conditional expectation of the cost, acting as a shadow price. The proof maps the problem into an auction-design form and links the optimum to a Bayesian persuasion problem, showing that under the paper's single-crossing conditions the optimal mechanism is a capped delegation scheme with interval censorship.","feed_headline":"Optimal no-transfer mechanism never requires the agent's report","feed_subtitle":"Disclosure plus delegation replaces transfers and keeps the agent's benefit private.","key_machinery":"The engine of the argument is the reduction of the two-sided no-transfer problem to a single-buyer auction design problem without private seller information. Define the allocation rule $X(t)=E[x(s,t)\\mid t]$ and the 'payment' rule $S(t)=E[s x(s,t)\\mid t]$, where $s$ is the cost; then Bayesian incentive compatibility is exactly the envelope condition $S(t)=S(0)+\\frac{1}{\\alpha}tX(t)-\\frac{1}{\\alpha}\\int_0^t X(\\tau)d\\tau$, and implementability without transfers is a pair of moment inequalities. The relaxed problem maximizes $\\int_0^1 X(t)v(t)\\,dt$ subject to $\\int_0^t X\\le \\int_0^t G_\\alpha$, where $v(t)=\\frac{1}{\\alpha}(1-F(t)-(1-\\alpha)t f(t))$ is the generalized virtual value and $G_\\alpha(t)=G(t/\\alpha)$ is the allocation of the agent's preferred mechanism. The central identity is $V(y)=\\int_y^1 v(\\tau)d\\tau$, the principal's payoff from full-information delegation. A convex-analytic dual — the equality between $\\max_X\\int V\\,dX$ and $\\min_{P\\ge V,\\ P\\ \\text{non-increasing convex}} \\int P\\,dG_\\alpha$ — connects the mechanism design problem to Bayesian persuasion and yields the optimal 'price function' $P$; from this, the optimal mechanism is read off as a capped delegation scheme with interval censorship.","core_discovery":"The discovery is that the principal-optimal mechanism in a no-transfer, two-sided private information problem can be taken to be 'report-free': the agent never tells the principal his benefit. The optimum is either a unilateral rejection (ignore the agent) or a delegation scheme in which the principal discloses her cost, possibly only as an interval, and the agent then chooses whether to implement. Because the agent's decision threshold is his conditional expectation of the partially internalized cost, disclosure acts as an instrument that replaces a transfer. Under single-crossing regularity, the optimal Bayesian mechanism is exactly the capped delegation mechanism with interval censorship, and the paper proves via convex duality that this mechanism attains the optimum.","pith_inferences":["Beyond the paper, if the interval-equivalence result holds more broadly, similar moment-based reductions may apply to no-transfer problems with multiple agents or with an agent's payoff that is a nonlinear function of the cost, where direct report-elicitation would be harder to analyze.","The 'information as price' mechanism suggests a testable organizational prediction: firms or regulators will often prefer to delegate decisions after coarse disclosures rather than demand detailed benefit reports, even when reporting is costless.","Because the construction relies on the independence of cost and benefit, the no-report conclusion should not be extrapolated to correlated environments, where the optimal mechanism may require keeping the principal's cost secret, as in a related setting the paper explicitly contrasts with.","The persuasion dual suggests a computational route: solve the mean-preserving-contraction problem to find the optimal censorship intervals for arbitrary densities, making the mechanism easy to implement numerically in applications."],"forward_implications":["The principal can implement the optimum without learning the agent's benefit, so the mechanism is privacy-preserving and immune to misreporting about the benefit.","Every mechanism, incentive compatible or not, is interim-equivalent to an interval mechanism; hence for any objective that depends only on the moments of the allocation, restricting to interval mechanisms entails no loss.","Under the single-crossing and convexity conditions, the optimal Bayesian incentive-compatible mechanism coincides with the optimal ex-post mechanism, so full disclosure and delegation suffice.","When the conditions for full transparency fail, interval censorship is optimal: the principal censors an interval of costs, replacing the realized cost by its conditional mean, thereby 'pricing' implementation above the benefit of low types.","The dual connects the no-transfer problem to Bayesian persuasion, so algorithms and characterizations for persuasion (e.g. monotone partitional contractions) directly produce optimal delegation mechanisms."],"supporting_citations":[{"why":"Supplies the envelope characterization of incentive compatibility used for the auction formulation.","marker":"Myerson, 1981"},{"why":"Provides the general envelope theorem used to derive the payment rule from the allocation rule in Lemma 3.","marker":"Milgrom and Segal, 2002"},{"why":"Establishes the persuasion duality the paper connects to; its monotone partitional solutions are used to construct the optimal mechanism in Corollary 2.","marker":"Dworczak and Martini, 2019"},{"why":"Gives a simpler strong-duality proof in linear persuasion, adapted in the proof of Theorem 2.","marker":"Dizdar and Kováč, 2020"},{"why":"Defines mean-preserving contractions and extreme points, used to formulate the set MPC(G_alpha) and monotone partitional contractions.","marker":"Kleiner et al., 2021"},{"why":"Introduces λ-regularity, used as a sufficient condition for the single-crossing and convexity properties of V.","marker":"Schweizer and Szech, 2019"},{"why":"Provides the rearrangement inequality used in Lemma 4 to characterize implementable payment rules via moment bounds.","marker":"Lieb and Loss, 2001"},{"why":"Shows that with correlated types the optimal mechanism requires keeping the principal's cost secret, marking the boundary of the paper's independence-based result.","marker":"Kattwinkel, 2020"}],"fun_headline_variants":["Optimal no-transfer mechanism: ignore or delegate, never ask","Free info and full authority beat asking the agent","Best mechanism asks nothing: reject or delegate with disclosure","Report-free optimality: disclose cost, then let agent decide","No reports needed: optimal mechanism is rejection or delegation"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument assumes that the principal's cost and the agent's benefit are drawn independently, so the agent's private benefit gives him no information about the cost he will face; if the two were correlated, the optimal mechanism could require the principal to keep her cost secret and the no-report conclusion could fail.","fun_headline_variants_meta":{"raw":{"variants":["Optimal no-transfer mechanism: ignore or delegate, never ask","Free info and full authority beat asking the agent","Best mechanism asks nothing: reject or delegate with disclosure","Report-free optimality: disclose cost, then let agent decide","No reports needed: optimal mechanism is rejection or delegation"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000357,"raw_usage":{"total_tokens":1819,"prompt_tokens":715,"completion_tokens":1104,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":331,"completion_tokens_details":{"reasoning_tokens":1025}},"tokens_in":331,"tokens_out":1104,"duration_ms":9364,"temperature":1.0,"reasoning_tokens":1025,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T17:45:21.596719+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take the paper's own Example 5 densities but perturb them so that $V$ crosses zero twice instead of once, and solve the relaxed problem (R) exactly; the paper's construction predicts the optimum is still attained by $X(t)=H(\\min\\{t_0,t\\})$ for a single $t_0$, while a true optimum that requires eliciting the agent's type would refute the abstract's broad claim.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the envelope characterization of incentive compatibility used for the auction formulation."},{"cited_title":"and Martini, G","cited_arxiv_id":null,"evidence_quote":"Establishes the persuasion duality the paper connects to; its monotone partitional solutions are used to construct the optimal mechanism in Corollary 2."},{"cited_title":"and Kov \\'a c , E","cited_arxiv_id":null,"evidence_quote":"Gives a simpler strong-duality proof in linear persuasion, adapted in the proof of Theorem 2."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines mean-preserving contractions and extreme points, used to formulate the set MPC(G_alpha) and monotone partitional contractions."},{"cited_title":"and Szech, N","cited_arxiv_id":null,"evidence_quote":"Introduces λ-regularity, used as a sufficient condition for the single-crossing and convexity properties of V."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the rearrangement inequality used in Lemma 4 to characterize implementable payment rules via moment bounds."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows that with correlated types the optimal mechanism requires keeping the principal's cost secret, marking the boundary of the paper's independence-based result."}],"review_version":1}