{"id":"ebcba83c-03c4-4b65-a90c-025fca58db3b","arxiv_id":"2502.00729","paper_version":2,"verdict":"REJECT","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"high","formal_verification":"none","parameter_count":0,"one_line_summary":"Selective response, withholding answers to drive users to human forums, can in a stylized model increase both GenAI revenue and user welfare, and near-optimal policies can be computed approximately.","lead":"A game-theoretic paper proposes that an AI assistant may strategically answer fewer questions, or answer less accurately, to push users to human forums like Stack Overflow, generating training data that improves the AI later. The authors show in a stylized model that this can raise both AI revenue and user welfare, and they provide approximation algorithms and regulatory conditions.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorem 5.1 is false for any positive threshold B, so the regulatory sufficient conditions in Section 6 do not follow from the stated result.","rationale":"The paper's central mechanism — selective response routes users to Forum, generating data that raises future GenAI quality and user proportions (Theorem 4.1) — is internally coherent under the model's explicit assumptions, and Observation 3.1 plus the simulations give genuine evidence for the qualitative possibility of mutual benefit. The weakest point is not the Forum-posting assumption (an explicit stylized choice) but the welfare-regulation theorem. Theorem 5.1 is stated for any strategy, yet it fails whenever some future round has x_t=0: welfare is equal, not lower, while wg_t(xτ)=0<B for any positive B. If B is allowed to be non-positive, Part 1 and Corollary 6.1 become vacuous, so the theorem cannot support the regulatory conclusions in Section 6. The reader's REJECT verdict is therefore justified. My independent concern is narrower but points to the same conclusion; the reader's listed weakest assumption differs, though their rationale already flags Theorem 5.1 as false. Even if one repaired the statement by requiring x_t>0, the proof's derivative argument remains incomplete: Part 2 needs h(y,x) to decrease on an interval near y=0, but dh/dy>0 for small x and y, so additional restrictions or a new proof are needed.","tokens_in":34368,"tokens_out":9596,"duration_ms":101704,"concrete_test":"Run the stated model with T=3, a(D)=1−e^{−0.4D}, ws=0.5, β=10, x=(0.1,0,1), τ=1, and xτ=(0,0,1). Compute w_2(xτ) and w_2(x): because x_2=0, both equal ws, while wg_2(xτ)=0. Any positive B>0 satisfies the premise of Theorem 5.1 Part 2 but violates its conclusion, directly falsifying the theorem as stated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Theorem 5.1, Part 2 fails for any positive threshold B. Take any instance and strategy x with x_t=0 for some t>τ — the paper's own Example 2.2 contains such rounds. Let xτ be a τ-selective modification, e.g., xττ<xτ. Since x_t=0, p_t(xτ)=p_t(x)=0, so w_t(xτ)=w_t(x)=ws, while wg_t(xτ)=0<B for every B>0. Part 2 asserts wt(xτ)<wt(x), a direct contradiction. The only escape is B≤0, but then Part 1's premise wgτ(x)<B is impossible because wgτ(x)≥0, making Corollary 6.1 vacuous. Section 6 and the claimed regulatory sufficient conditions rest on this theorem, so that contribution is unsupported by the stated result. This is an internal inconsistency, not a disagreement about modeling assumptions.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies a T-round model in which a GenAI platform chooses a selective response level x_t in [0,1] each round, users choose between GenAI and a human forum via a softmax rule, and users who do not receive an answer post on the forum and thereby generate training data for GenAI. The authors claim that selective response can Pareto-dominate always responding (Observation 3.1), that a one-round reduction in response strictly increases all future data and weakly increases future user shares (Theorem 4.1), and they propose approximation algorithms for revenue maximization (Theorems 4.4 and 4.6) and for welfare-constrained revenue maximization (Theorem 4.7). They then state a threshold theorem (Theorem 5.1) about the welfare effect of a single-round selective modification, and use it to derive regulatory sufficient conditions (Corollary 6.1) and a revenue-gap bound (Corollary 6.2). The paper concludes with a discussion of modeling limitations and simulations over cutoff strategies.","tokens_in":1966,"tokens_out":2320,"duration_ms":196579,"significance":"The model is original and the core monotonicity result, Theorem 4.1, is a nontrivial formal observation that could be useful for later work on GenAI-data ecosystems. The paper is also commendably explicit about its key assumption that unanswered users post on the forum, and the ASR algorithm is presented with concrete approximation and runtime guarantees. However, the advertised regulatory and constrained-optimization contributions rest on results that are false or invalid as stated: Theorem 5.1(2) is contradicted by zero-response rounds, Corollary 6.2 has a sign error, and the reduction behind Theorem 4.7 uses negative rewards in a framework that requires nonnegative rewards. These are load-bearing errors, not presentation issues, and they undermine the paper's central claims about welfare regulation and constrained revenue maximization.","major_comments":[{"comment":"Part 2 of Theorem 5.1 is false for any positive threshold B. Take any strategy x with x_t = 0 for some t > \\tau, as in Example 2.2, and any \\tau-selective modification x^\\tau. Since x^\\tau_t = x_t = 0, we have w^g_t(x^\\tau) = a(D_t(x^\\tau)) * 0 = 0 < B for every B > 0, but w_t(x^\\tau) = w_t(x) = w_s, contradicting the strict inequality. The proof in Appendix D does not repair this: its derivative argument establishes negativity of dh/dy only for negative accuracy values (the auxiliary function is analyzed as y to -infinity), whereas accuracy is confined to [0,1], and the proof never actually constructs the threshold B. The only way to avoid the counterexample is B <= 0, but then Part 1's hypothesis w^g_\\tau(x) < B is impossible since w^g_\\tau(x) >= 0, making Corollary 6.1 vacuous. Consequently, the regulatory sufficient conditions in Section 6 do not follow from the stated theorem.","section":"Section 5, Theorem 5.1(2) and Appendix D"},{"comment":"The displayed bound in Corollary 6.2 contains a sign error. The proof's derivation produces L_r(p_\\tau(x) - p_\\tau(x^\\tau)) times the sum of gamma^t from t = \\tau+1 to T, which is nonnegative and is bounded above by L_r gamma^\\tau (p_\\tau(x) - p_\\tau(x^\\tau))/(1 - gamma). The corollary instead states the second term as L_r gamma^\\tau (p_\\tau(x^\\tau) - p_\\tau(x))/(1 - gamma), which is negative for any \\tau-selective modification. As printed, the right-hand side is negative, while U(x^\\tau) - U(x) can be positive; for instance, with T = 2, a(D) = 0.4D, w_s = 0.5, beta = 10, r(p) = p^2, gamma = 1, and x = (1,1), the \\tau = 1 modification x^\\tau = (0,1) satisfies Assumption 2.1 and gives U(x^\\tau) > U(x). The revenue-gap bound in Section 6.2 is therefore false as stated.","section":"Section 6.2, Corollary 6.2 and Appendix E.1"},{"comment":"The reduction of the welfare-constrained problem to PARS-MDP is invalid as written. The second reward function is defined as W(s^d_t, y) = floor(y q(d,y)(a(d) - w_s))_epsilon, which takes negative values whenever a(d) < w_s, but the PARS-MDP framework used in the proof (and in reference [3]) requires nonnegative rewards R_A, R_P : S x A to R_{\\ge 0}. Likewise, the budget B is defined through W_1 = W - T w_s, which can be negative, while the PARS-MDP budget is required to be nonnegative. A constant shift of the welfare reward would be needed to make the reduction valid, but no such shift is introduced or analyzed. Hence the constraint encoding and the guarantees of Theorem 4.7 are not established.","section":"Section 4.3 and Appendix C.3, Theorem 4.7"},{"comment":"Corollary 6.1 is stated without a proof, and it does not follow from Theorem 5.1 as stated. Under the commitment condition, the 'gray' rounds covered by Part 2 are impossible: for any t > \\tau with w^g_t(x) > 0, the commitment gives w^g_t(x) > C >= B, and since w^g_t(x^\\tau) >= w^g_t(x), Part 2's hypothesis w^g_t(x^\\tau) < B cannot hold; for w^g_t(x) = 0, we have x_t = 0 and the two welfare values coincide. Thus the intended 'positive area exceeds negative area' argument is not captured by the theorem, and the corollary needs a separate proof. The appendix does not supply one, so the Section 6.1 welfare-improvement claim is currently unsupported.","section":"Section 6.1, Corollary 6.1"}],"minor_comments":[{"comment":"The paper repeatedly claims to derive 'sufficient and necessary conditions' for selective response to improve welfare, but Section 6 contains only sufficient conditions and no necessary condition is stated or proved.","section":"Abstract and Introduction"},{"comment":"In the proof of Theorem 4.4, U_t(x) is defined as the sum from i=t to T of gamma^{i-t} p_i(x), but the revenue objective is U(x) = sum_t gamma^t r(p_t(x)); the proof should use r(p_i) for consistency.","section":"Appendix C.2, Theorem 4.4 proof"},{"comment":"Corollary 6.2 does not state an assumption that gamma < 1, yet the displayed bound contains a factor 1/(1-gamma) and is undefined at gamma = 1, a case that the paper considers elsewhere.","section":"Section 6.2, Corollary 6.2"},{"comment":"In the proof of Proposition 3.2, the sigmoid function is defined using q(T-1,1) and q((T-1)/2,1), but the subsequent displayed expressions sometimes write q(T-1) without the second argument, which makes the construction hard to follow.","section":"Appendix B.1, Proposition 3.2 proof"},{"comment":"The text refers to the 'PARSE-MDP problem' in one place and to 'PARS-MDP' elsewhere; the terminology should be made consistent with reference [3].","section":"Appendix C.3, Step 4"}],"recommendation":"reject","confidential_remarks":"The paper contains promising ideas and several correct-looking components (notably Observation 3.1, Theorem 4.1, and the ASR approximation analysis), but the false Theorem 5.1, the sign error in Corollary 6.2, and the invalid PARS-MDP reduction are load-bearing and currently make the paper's advertised regulatory and constrained-optimization contributions untenable. A resubmission that corrects Sections 5-6 and Appendix C.3, and that gives a genuine proof of Corollary 6.1, would merit reconsideration."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know that this paper introduces a genuinely new idea—selective response as a strategic tool for GenAI to feed human forums and build future data—and the basic existence results hold up. But the regulatory half of the paper rests on a theorem that is false, and that is not a minor glitch.\n\nWhat is actually new: the framing of selective response as a way to escape the negative feedback loop where GenAI kills the forums it depends on, and a clean dynamic model of users choosing between GenAI and a human forum. Observation 3.1 shows selective response can Pareto-dominate always-responding, and Theorem 4.1's compounding effect (more data today means more users tomorrow) is plausible and correctly proved. The price-of-always-responding bounds in Section 3 are also interesting and, as far as I checked, sound.\n\nThe soft spot is Theorem 5.1, Part 2. The stress-test counterexample is right: take any base strategy x with x_t = 0 for some t > τ. Then a τ-selective modification xτ also has xτ_t = 0, so wg_t(xτ) = wg_t(x) = 0 < B, and w_t(xτ) = w_t(x) = ws—not strictly less. So Part 2 fails for every positive B, and the only way to rescue it would be to set B ≤ 0, which makes Part 1 vacuous. Section 6's Corollary 6.1 and the regulatory sufficient conditions are built directly on this, so that contribution is unsupported. The welfare-constrained revenue algorithm in 4.3 also leans on a self-cited PARS-MDP result, but that is a lesser concern compared to a false theorem at the core of the regulatory story.\n\nWho gets value from this: people working on AI economics, platform competition, and information design. The concept is worth discussing, and the model up to Section 4 is a useful starting point. The paper deserves a serious referee, but it needs a major revision: fix or restate Theorem 5.1, rework Section 6, and verify the PARS-MDP dependence. I would send it out, but I would not rely on the regulatory conclusions as they stand.","headline":"Genuinely new idea and a solid dynamic model, but the regulatory centerpiece (Theorem 5.1) is false as stated, so the paper needs major revision before it can be trusted.","tokens_in":35063,"tokens_out":2074,"would_cite":false,"duration_ms":23408,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A GenAI service can increase its long-term revenue and user welfare by deliberately withholding or degrading answers on emerging topics, because the users it turns away generate training data on human forums.","keywords":["selective response","generative AI","data accumulation","user welfare","revenue maximization","online Q&A forums","game theory"],"falsifier":"Instrument a deployed GenAI service that withholds answers on a new topic and measure the fraction of denied users who actually post on the partner forum within a week; if that fraction is a constant $q<1$, the recurrence becomes $D_{t+1}=D_t+q(1-p_t)$, the strict data gain in Theorem 4.1 shrinks proportionally, and for small $q$ one can exhibit parameter ranges in which no selective strategy beats always-responding.","tokens_in":34181,"feed_emoji":"🤐","tokens_out":11765,"duration_ms":114390,"temperature":0.7,"pith_summary":"This paper tries to establish that a generative-AI platform should sometimes not answer: on emerging topics it withholds answers or offers deliberately lower-quality ones, steering users to human Q&A forums. The paper argues this short-term sacrifice compounds: each denied user who posts on a forum creates a unit of training data, which improves GenAI accuracy, which attracts more users next round, which generates still more data. In the model, reducing the answer level in any single round strictly increases cumulative data in all later rounds and weakly increases the share of users who choose GenAI; there are instances where this dominates always-responding on both revenue and welfare. The paper also gives an approximately optimal revenue-maximizing algorithm and regulatory conditions under which one forced round of selective response raises welfare with bounded revenue loss.","feed_headline":"Withholding answers can raise GenAI revenue and user welfare","feed_subtitle":"Turned-away users post on human forums, adding data that makes the AI more profitable later","key_machinery":"The engine is the one-round data-update map: starting with cumulative data $D$ and response level $x$, next-round data is $D + (1 - p(D,x))$, where $p(D,x)$ is the softmax share of users who receive an answer from GenAI. The paper proves that under Assumption 2.1 this map is strictly increasing in $D$; since a lower $x$ in a round means more users go to the human forum, the map turns one denied query into strictly more data in every later round. Iterating that monotonicity is Theorem 4.1, and all later results—the dominance comparison, the approximation guarantees, and the regulator's thresholds—ride on it.","core_discovery":"The core claim is formalized as Theorem 4.1: fix any strategy $x$ and any round $\\tau$; a $\\tau$-selective modification that lowers the answered fraction in round $\\tau$ yields strictly more cumulative data $D_t$ in every later round $t>\\tau$, and weakly higher user proportions $p_t$, with equality only in degenerate zero-response states. Because $D_t$ drives GenAI quality through the accuracy function $a(D_t)$, and user choices respond to quality through the softmax, this data advantage is self-reinforcing. The theorem is the reason selective response can dominate the always-responding strategy on revenue and welfare simultaneously (Observation 3.1), why the price of always responding is unbounded in revenue and arbitrarily close to 2 in welfare, and why both the revenue-maximization and welfare-constrained algorithms work.","pith_inferences":["A testable corollary the paper does not spell out: deployment logs of a selective-response service should show answer rates starting near zero on a new topic, then jumping upward as forum data accumulates; the timing of that jump should track the accuracy function's Lipschitz constant.","The model equates saying nothing with giving a lower-quality answer; separating the two would change the revenue calculus, because a visibly wrong answer can damage trust in a way silence does not, and an optimal policy would likely favor explicit disclaimers over incorrect content.","The same control problem arises inside a single organization: an AI assistant that defers hard queries to a human annotation queue is effectively choosing a selective-response schedule, so the paper's monotonicity result suggests how to tune deferral thresholds under a data-accumulation objective."],"forward_implications":["Reducing the answer level in any single round strictly increases cumulative data in all later rounds and weakly raises future user proportions, so a sufficiently patient GenAI can trade a little current engagement for a permanently larger future user base.","The price of always responding is unbounded in revenue: for any $M$ there is an instance where the best selective strategy earns more than $M$ times the always-responding revenue.","Welfare under the best selective strategy can be made arbitrarily close to double the always-responding welfare.","An approximately optimal revenue-maximizing strategy can be found by dynamic programming on a discretized data state, with additive error $\\epsilon L_r T^2$ and runtime $O(T^2|A|/\\epsilon)$; a grid over $[0,1]$ extends the guarantee to continuous strategies.","A regulator who sees only past actions can force a one-round answer reduction that raises total welfare whenever current answered-utility is below one threshold and the platform commits to future utility above a second threshold, with the revenue loss bounded."],"supporting_citations":[{"why":"Supplies evidence that large language models reduce public knowledge sharing on Q&A platforms, motivating the negative feedback loop the paper targets.","marker":"[13]"},{"why":"Documents the consequences of generative AI for online knowledge communities, supporting the premise that GenAI traffic displaces forum contributions.","marker":"[7]"},{"why":"Provides coding-Q&A evidence that generative AI changes user contribution behavior, grounding the data-accumulation mechanism.","marker":"[32]"},{"why":"The closest prior model of GenAI training and user welfare, against which the selective-response model positions its contribution.","marker":"[45]"},{"why":"Supplies the principal-agent MDP reduction used to solve the welfare-constrained revenue-maximization problem with formal guarantees.","marker":"[3]"}],"fun_headline_variants":["Withholding AI answers boosts revenue and welfare","Selective non-answers increase GenAI profit","Strategic curbs on AI answers pay off later","AI profits from steering users to human forums","Less AI hand-holding, more long-term gains"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The model assumes that every user who is denied an answer posts their question on the human forum, contributing one unit of data; if denied users instead leave or simply abandon the question, the compounding data engine that makes selective response beneficial disappears.","fun_headline_variants_meta":{"raw":{"variants":["Withholding AI answers boosts revenue and welfare","Selective non-answers increase GenAI profit","Strategic curbs on AI answers pay off later","AI profits from steering users to human forums","Less AI hand-holding, more long-term gains"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000362,"raw_usage":{"total_tokens":1912,"prompt_tokens":860,"completion_tokens":1052,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":476,"completion_tokens_details":{"reasoning_tokens":982}},"tokens_in":476,"tokens_out":1052,"duration_ms":10841,"temperature":1.0,"reasoning_tokens":982,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-09T17:58:27.733424+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Instrument a deployed GenAI service that withholds answers on a new topic and measure the fraction of denied users who actually post on the partner forum within a week; if that fraction is a constant $q<1$, the recurrence becomes $D_{t+1}=D_t+q(1-p_t)$, the strict data gain in Theorem 4.1 shrinks proportionally, and for small $q$ one can exhibit parameter ranges in which no selective strategy beats always-responding.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies evidence that large language models reduce public knowledge sharing on Q&A platforms, motivating the negative feedback loop the paper targets."},{"cited_title":"Burtch, D","cited_arxiv_id":null,"evidence_quote":"Documents the consequences of generative AI for online knowledge communities, supporting the premise that GenAI traffic displaces forum contributions."},{"cited_title":"Li and K","cited_arxiv_id":null,"evidence_quote":"Provides coding-Q&A evidence that generative AI changes user contribution behavior, grounding the data-accumulation mechanism."},{"cited_title":"Ben-Porat, Y","cited_arxiv_id":null,"evidence_quote":"Supplies the principal-agent MDP reduction used to solve the welfare-constrained revenue-maximization problem with formal guarantees."}],"review_version":1}