{"id":"3b627c13-5bdd-4608-bc6a-7e402eeb26b5","arxiv_id":"2507.09473","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A primal-dual mechanism with lazy dual updates, randomized exploration, and a fixed-point optimistic learning rule achieves Õ(√T) regret with near-truthful strategic agents under long-term constraints.","lead":"The paper designs an incentive-aware mechanism for dynamically allocating a reusable resource to self-interested agents under long-term cost constraints, achieving near-optimal social welfare regret while keeping agents close to truthful. It matters because it shows that robustness to strategic misreporting can be added to standard primal-dual allocation methods at essentially no asymptotic efficiency cost.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The main equilibrium proof omits the feasibility-rejection safeguard: a unilateral deviation can trigger Line 14 and erase the exploration-round penalty, so Lemma B.3 and the PBE existence argument apply to a mechanism without the constraint-enforcement rule, not to Algorithm 2 as stated.","rationale":"The reader's weakest assumption was the γ-impatient model, but that is a modeling choice and, for fixed γ∈(0,1), the dependence of the final bound on γ is only a constant. The more load-bearing issue is that the equilibrium proof analyzes a relaxed mechanism without the feasibility rejection. Algorithm 2's Line 14 changes the payoff structure off the equilibrium path: a deviating agent can trigger a rejection and avoid the negative payment that the exploration penalty assumes. The paper's own stopping-time argument only guarantees no rejection on the equilibrium path, not along deviating histories. Therefore the PBE existence theorem is not proven for the algorithm as specified. This concern is concrete and testable via a simple two-round instance. It does not necessarily falsify the result; a more careful argument might handle rejected rounds, so the appropriate disposition remains conditional: the paper needs a revision that incorporates Lines 13-14 into the incentive analysis. The reader's verdict of CONDITIONAL therefore stands, but for a different and more substantive reason than the γ-impatience assumption.","tokens_in":52686,"tokens_out":24581,"duration_ms":312341,"concrete_test":"Analyze a minimal instance with T=2, K=2, d=1, ρ=0.5: suppose round 1 allocates to agent 1 and consumes the entire budget, and round 2 is an exploration round for agent 2 whose true value is 0. Compare agent 2's expected utility from reporting 1 under (a) the no-rejection mechanism of Lines 4-12 and (b) Algorithm 2 with Line 14 active. If in case (b) the allocation is rejected and the agent gets utility 0, while in case (a) the agent receives negative utility, then the exploration penalty used in Lemma B.3 is not present in the stated mechanism. Verifying this single instance settles whether the penalty argument survives the feasibility-safeguard rule.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that Algorithm 2 admits a PBE with near-truthful reports and Õ(√T) regret. The incentive analysis rests on Lemma B.3, which is stated for the \"epoch-ℓ game with exploration rounds specified by Lines 4 to 12\" of Algorithm 2. Those lines do not include Lines 13-14, the cumulative-cost rejection rule. The proof uses the stopping time Tv to argue that Line 14 has no effect, but Tv is defined along the equilibrium path; a unilateral deviation changes the cumulative cost and can make Line 14 trigger earlier. When Line 14 rejects a tentative allocation, the agent receives utility 0 instead of the negative utility (v−p) that the exploration-round penalty relies on. In particular, the proof's lower bound on the current-epoch difference, which uses the exploration loss −(u−v)²/(2K|E_l|), is computed in a game where no rejection can occur. With rejection present, a large misreport in an exploration round can be followed by rejection, making the immediate penalty vanish. Thus the key inequality preceding Eq. (17) is not justified for Algorithm 2 as stated, and the existence of the PBE π* asserted in Theorem B.5 and used in Theorem A.2 is not established. This is a substantive gap in the equilibrium proof, independent of the γ-impatience assumption and of the notation mismatches flagged by the reader.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies repeated allocation of a single indivisible resource among K strategic agents over T rounds, under d long-term cost constraints. Agents hold private values and observe public costs; the planner knows neither value nor cost distributions. The authors propose the Incentive-Aware Primal-Dual (IAPD) framework combining epoch-based lazy dual updates, VCG-style adjusted payments, randomized exploration rounds, and a cumulative-cost rejection safeguard. Two dual-update rules are analyzed: FTRL and a novel Optimistic FTRL with Fixed Points (O-FTRL-FP). The paper claims, under a γ-impatient agent model and a smooth-cost assumption, the existence of a Perfect Bayesian Equilibrium with near-truthful reports, zero long-term constraint violation, and regret Õ(T^{2/3}) for FTRL and Õ(√T) for O-FTRL-FP, the latter matching the non-strategic lower bound up to polylogarithmic factors.","tokens_in":52882,"tokens_out":10416,"duration_ms":124616,"significance":"If correct, the √T regret guarantee under strategic behavior would be a notable contribution, indicating that incentive compatibility can be obtained at negligible asymptotic cost in constrained online allocation. The O-FTRL-FP fixed-point oracle is a novel and interesting technical device, and the appendix provides an extensive proof skeleton with several sophisticated concentration arguments (e.g., Lemmas C.4–C.8). The numerical study is a further strength. However, the main equilibrium theorem relies on an incentive analysis that explicitly excludes the mechanism's own feasibility-rejection rule when evaluating deviations, and this gap must be closed before the central claims are fully supported.","major_comments":[{"comment":"The incentive analysis is conducted in the 'epoch-ℓ game with exploration rounds' specified by Lines 4 to 12 of Algorithm 2, i.e., without the cumulative-cost rejection rule in Lines 13–14. The proof of Theorem B.5 argues that Line 14 'has no effect' because of the stopping time T_v, but T_v is defined using the equilibrium path allocations. A unilateral deviation can change the cumulative cost process, so Line 14 can trigger at a round t ≤ T_v (where T_v is evaluated under π*) and reject the tentative allocation. When a tentative allocation is rejected, the agent receives utility 0 rather than v−p, so the exploration-round penalty −(u−v)²/(2K|E_ℓ|) used in the proof of Lemma B.3 is not incurred. Consequently, the key inequality preceding Eq. (17) is not justified for Algorithm 2 as stated, and the existence of the PBE π* asserted in Theorem B.5 (and used in Theorems 3.1 and 3.2) is not established. The proof needs to handle deviations that cause earlier triggering of Line 14, or the mechanism must be modified so that the rejection rule does not remove the exploration penalty.","section":"Appendix B.2, Lemma B.3 and proof of Theorem B.5"},{"comment":"Line 12 of Algorithm 2 allocates to argmax_i ũ_{t,i} with the maximization implicitly over agents i ∈ [K], while the analysis (Lemma B.1, the definition of e_i*_t in Eq. (13), and the benchmark in Eq. (2)) uses argmax over {0}∪[K], treating forfeiture as a dummy agent with zero value and zero cost. If the mechanism cannot forfeit in standard rounds, the payment becomes the second-highest among the K agents rather than max(0, second-highest), and the truthfulness argument in Lemma B.1 no longer applies. The algorithm should explicitly include the dummy option in the argmax, with forfeiture when the dummy wins, or the analysis must be reworked for a mechanism restricted to [K].","section":"Algorithm 2, Line 12 vs. Section 2.1 and Lemma B.1"},{"comment":"The theorem statement sets L = T^{1/3} and epoch length |E_ℓ| = T/L = T^{2/3}, but the proof's balancing step states 'Setting L = T^{2/3} and |E_ℓ| = T^{1/3}' and the subsequent regret calculation uses that choice. The statement should be corrected to L = T^{2/3}, |E_ℓ| = T^{1/3} to match the proof and the claimed Õ(T^{2/3}) regret. As written, the formal statement is internally inconsistent.","section":"Appendix A.1, Theorem A.1"}],"minor_comments":[{"comment":"The definition of M_ℓ in Theorem A.2 depends on parameters ε and δ that are not specified in the theorem statement. The proof later sets ε = 1/(√T K²ε_c) and δ = 1/(6dT); these values (or an explicit statement that they are arbitrary constants) should be included in the theorem statement so that the regret bound is well-defined.","section":"Appendix A.2, Theorem A.2"},{"comment":"The text 'more preciously' should read 'more precisely'.","section":"Section 4.2.5"},{"comment":"In the displayed inequality in the proof of Theorem B.5, the term '3|E_ℓ|/|E_ℓ|' is equal to 3 and appears to be a typographical artifact; it should be written as the additive constant 3 from the union bound over the three failure events.","section":"Appendix B.2, Eq. (20)"},{"comment":"When Line 14 rejects the tentative allocation by setting i_t = 0, the payment p_{t,i_t} for the tentative winner is not explicitly set to zero. The pseudocode should state that the payment is also canceled to avoid ambiguity.","section":"Algorithm 2, Line 14"},{"comment":"In the definition of the stopping time T_v, the term '+1' should be written as the vector 1 ∈ R^d (or explicitly 'coordinate-wise +1') to avoid confusion between scalar and vector addition.","section":"Eq. (14)"},{"comment":"The title in the running header ('Efficiency, Feasibility, and Incentive-Awareness in Constrained Online Resource Allocation') differs from the title on the first page and in the abstract ('Incentive-Aware Dynamic Resource Allocation under Long-Term Cost Constraints'). The paper should use one consistent title.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The paper is ambitious and the appendices are unusually detailed, but the core equilibrium proof has a genuine off-path gap: the feasibility-rejection rule in Algorithm 2 is excluded from the incentive analysis, while the stopping-time argument used to dismiss it is only valid on the equilibrium path. This is a load-bearing issue for both main theorems. The parameter inconsistency in Theorem A.1, while readily fixable, indicates the need for a careful pass over the formal statements. I recommend major revision rather than rejection because the underlying approach may be repairable (e.g., by extending Lemma B.3 to the mechanism with rejection, or by bounding the effect of the rejection region on the exploration penalty) and the O-FTRL-FP machinery is a promising contribution in its own right."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Top line: this is a serious paper with a big-ish claim — that strategic behavior can be made asymptotically free in constrained online allocation — and the main proof has a real hole that the authors have not acknowledged. The novel machinery (epoch-based lazy dual updates, randomized exploration rounds, and the O-FTRL-FP fixed-point oracle) is genuinely new relative to Yin et al. 2022, and the appendix is unusually detailed. The high-level architecture is plausible: lazy updates suppress inter-epoch manipulation, exploration creates local penalties, and the optimistic fixed-point update exploits near-i.i.d. structure to beat the T^{2/3} barrier.\n\nWhat the paper does well: the decomposition into PrimalAlloc and DualVar is clean; Lemmas B.3–B.5 and C.4–C.8 form a coherent skeleton; and the numerical section, while not a proof, supports the qualitative claim. The paper also positions itself honestly relative to Yin et al.\n\nThe soft spots are real. First, the stress-test lands. Lemma B.3 and Theorem B.5 analyze the epoch game without Lines 13–14. The argument that the stopping time Tv makes the rejection rule irrelevant works only on the equilibrium path; a unilateral deviation can change cumulative costs and make Line 14 trigger, so the exploration-round penalty can vanish and the inequality leading to Eq. (17) is not justified for Algorithm 2 as stated. That is a load-bearing gap in the PBE existence proof, not a cosmetic one. Second, the reader's three mechanical flags are accurate: Algorithm 2's standard round maximizes over [K] while the analysis uses {0}∪[K]; Theorem A.1 states L=T^{1/3} and |E_ℓ|=T^{2/3} but the proof uses L=T^{2/3}, |E_ℓ|=T^{1/3}; and the fixed-point oracle is proven non-constructively while the Section 5 approximation is not shown to preserve the theoretical bound. The first two are probably fixable typos; the third matters for implementability. Third, γ-impatience and smooth costs are strong assumptions; as γ approaches 1 the key bound diverges, and the paper is quiet about how essential that is. The allowance of negative payments under the money-burning framing also deserves more discussion.\n\nNone of this kills the project; the central idea is probably right. But as written, the manuscript does not establish the theorem for the stated mechanism. The authors should be asked to fix the rejection-rule analysis (or explicitly restrict the theorem to a variant without feasibility enforcement), reconcile the epoch parameters, and specify an approximation of the fixed point that preserves the regret.\n\nThis deserves serious refereeing, not desk rejection. I would focus a referee on the Line 14 gap first. I would not cite the sqrt(T) PBE claim until that fix survives.","headline":"A serious paper with a genuinely new mechanism and a plausible high-level story, but the PBE proof has a load-bearing gap involving the cost-feasibility rejection rule, and several smaller mechanical errors need fixing before the main theorem is credible for Algorithm 2 as stated.","tokens_in":53579,"tokens_out":2620,"would_cite":false,"duration_ms":32684,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["91B32","68W27","91A26"],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper argues constrained online resource allocation can tolerate strategic agents at no polynomial-order cost: Õ(√T) regret matching the non-strategic lower bound, exact long-term constraints, and near-truthful reports in equilibrium.","keywords":["online resource allocation","primal-dual algorithms","strategic agents","incentive compatibility","perfect Bayesian equilibrium","optimistic online learning","regret bounds","long-term constraints"],"falsifier":"Run the mechanism with nearly patient agents ($\\gamma = 1$ or $\\gamma = 1 - 1/T$), let them learn their reports with a high-capacity algorithm over thousands of repetitions, and measure whether large misreports persist and whether the average regret stays at $\\widetilde{O}(\\sqrt{T})$. A sharper targeted check comes from the paper's own Lemma B.3: in the two-agent identical-value example of Example 4, evaluate the inequality that must hold between the exploration loss ($1/(2K|E_\\ell|^3)$) and the discounted manipulation benefit; the regime where $\\gamma^{s_{\\ell+1}}/(1-\\gamma)$ exceeds that loss is precisely where the paper's proof no longer guarantees near-truthfulness.","tokens_in":52277,"feed_emoji":"⚖️","tokens_out":11769,"duration_ms":120057,"temperature":0.7,"pith_summary":"This paper asks whether a planner can allocate a scarce reusable resource — think cloud GPUs or mobile health units — to self-interested agents who may misreport their private valuations, while simultaneously maximizing social welfare, obeying multi-dimensional long-term cost constraints, and keeping agents roughly honest. The authors argue that the standard primal-dual method, the workhorse of constrained online allocation, is fragile in such strategic settings: agents learn to distort their reports to move future 'shadow prices' (dual variables) in their favor. Their incentive-aware mechanism neutralizes this manipulation with three coordinated ingredients — epoch-based lazy dual updates, VCG-style payments, and randomized exploration rounds that impose an immediate utility loss on liars. With a new optimistic online-learning subroutine that resolves a fixed-point dependency between prices and allocations, the mechanism achieves $\\widetilde{O}(\\sqrt{T})$ social-welfare regret with exactly zero long-term constraint violation, matching the $\\Omega(\\sqrt{T})$ lower bound of the non-strategic problem. The upshot, if the main theorem holds, is that protecting against strategic behavior need not cost efficiency, provided agents discount the future.","feed_headline":"Õ(√T) regret is achievable even when agents lie","feed_subtitle":"Lazy price updates plus random price checks keep agents near-truthful while all cost constraints hold exactly.","key_machinery":"Three components carry the argument. (1) Epoch-based lazy updates: the dual variable $\\lambda_\\ell$ is fixed for the whole epoch $E_\\ell$, so any single misreport has limited and delayed influence on future shadow prices. (2) A boosted second-price payment rule: the winner pays their dual-weighted cost plus the runner-up's adjusted report, making truthful reporting weakly dominant in the one-shot epoch game (Lemma B.1, Theorem B.2). (3) Randomized exploration rounds: with probability $1/|E_\\ell|$ the mechanism offers a uniformly random price to a random agent, giving any misreport an expected immediate loss of order $(u-v)^2/(K|E_\\ell|)$; Lemma B.3 shows this outweighs the $\\gamma$-discounted future benefit of manipulating the next dual, so large misreports occur in only $\\widetilde{O}(1)$ rounds per epoch. The dual-side novelty is O-FTRL-FP (Eq. (6)), which adds an optimistic prediction term $\\widetilde{g}_\\ell(\\lambda_\\ell)^\\top \\lambda$ — an estimate of the coming epoch's loss built from past reports — to the FTRL objective. Because the prediction depends on $\\lambda_\\ell$ through an argmax, the update is a fixed-point problem: the paper proves existence of approximate fixed points via a partition-of-unity (Brouwer) argument under an approximate-continuity condition (Lemmas C.4, C.5), and then bounds the three stability errors — allocation mismatch, empirical estimation, and untruthful reports (Lemmas C.6–C.8).","core_discovery":"The paper's central claim is Theorem 3.2 (formalized as Theorem A.2): under Assumptions 1 and 3, Algorithm 2 with the O-FTRL-FP dual update guarantees the existence of a Perfect Bayesian Equilibrium strategy profile $\\pi^*$ under which the social-welfare regret relative to the offline optimal allocation is $R_T(\\pi^*, \\text{Algorithm 2}) = \\widetilde{O}(\\sqrt{T})$ and the long-term constraint violation is $B_T = 0$. The regret rate matches, up to logarithmic factors, the $\\Omega(\\sqrt{T})$ lower bound for the non-strategic version of the problem, so incentive compatibility comes at essentially no polynomial-order cost. The near-truthfulness of the equilibrium is what unlocks the faster rate: agents rarely misreport by more than $1/|E_\\ell|$, so the planner can treat historical reports as approximately true signals, predict the loss of any candidate dual vector, and run an optimistic online learner. Plain FTRL cannot reach this rate, because the epoch structure needed for incentive compatibility triggers an $\\Omega(T^{2/3})$ switching-cost barrier (Theorem 4.4) that only breaks once the losses acquire an almost-i.i.d. structure from truthful reports.","pith_inferences":["The stabilise-then-predict recipe — freeze prices, punish deviations, then exploit the cleaner signal for optimistic learning — likely transfers to other settings where learning and incentives conflict, such as repeated auctions with budgets or procurement with strategic suppliers.","The O-FTRL-FP subroutine is a reusable primitive: an optimistic learner for decision-dependent, discontinuous loss predictions, applicable beyond mechanism design wherever the loss gradient depends on the chosen action through an argmax.","For nearly patient agents the paper's guarantees are silent; a testable extension would scale the exploration probability with $1/(1-\\gamma)$ and check numerically how the regret constant degrades as $\\gamma \\to 1$.","The simulation suggests a stronger conjecture than the theorem: Q-learning agents not only live alongside a truthful equilibrium but converge to it; measuring convergence rates under different exploration schedules would settle this."],"forward_implications":["A planner can add robustness to strategic misreporting at no polynomial-order cost: $\\widetilde{O}(\\sqrt{T})$ regret with exact constraint satisfaction, against the $\\Omega(\\sqrt{T})$ lower bound in the truthful-agent benchmark.","Because agents are near-truthful in equilibrium, the planner's historical reports become trustworthy samples, which is what makes optimistic dual prediction possible and upgrades the rate from $T^{2/3}$ to $\\sqrt{T}$.","The mechanism satisfies long-term constraints exactly ($B_T = 0$), since any allocation that would push cumulative cost past the budget is rejected immediately.","The epoch-based lazy update is necessary for incentives and sufficient for learning only in combination with exploration; the paper formalizes the trade-off as an $\\Omega(T^{2/3})$ low-switching barrier for plain FTRL.","The framework extends to multi-unit multi-demand allocation, so the design principles carry beyond one-item-per-round settings."],"supporting_citations":[{"why":"The non-strategic primal-dual baseline whose Algorithm 1 is the vulnerable benchmark and whose regret framework the paper extends to strategic agents.","marker":"Balseiro et al. (2023)"},{"why":"Supplies the $\\gamma$-impatient agent model (Assumption 1) and the inter-epoch manipulation-bounding technique used in Lemma B.3.","marker":"Golrezaei et al. (2021a; 2023)"},{"why":"Provides the Optimistic FTRL template that O-FTRL-FP extends to decision-dependent predictions.","marker":"Rakhlin and Sridharan (2013)"},{"why":"Establishes the $\\Omega(\\sqrt{T})$ non-strategic lower bound that Theorem 3.2 near-matches.","marker":"Arlotto and Gurvich (2019)"},{"why":"Gives the low-switching hardness (Theorem 4.4) that forces the $\\Omega(T^{2/3})$ barrier for plain FTRL and motivates the optimistic fixed-point design.","marker":"Dekel et al. (2014)"},{"why":"Prior work on strategic agents in online allocation with homogeneous agents and fair-share constraints, which this paper generalizes.","marker":"Yin et al. (2022)"},{"why":"The FTRL-FB idea of predicting through fixed points, adapted here to discontinuous argmax-based predictions.","marker":"Zimmert and Lattimore (2022)"}],"fun_headline_variants":["Near-optimal regret even when agents lie","Strategic agents cost nothing in online allocation","Lying agents can't sacrifice efficiency in this online mechanism","Incentive-aware online allocation hits non-strategic bound","Mechanism matches lower bound despite strategic reports"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is Assumption 1: every agent maximizes a $\\gamma$-discounted payoff over the whole game, for a fixed discount factor $\\gamma \\in (0,1)$, and the guarantee degrades if agents are nearly patient, because the bound on the future benefit of manipulating the next epoch's dual is proportional to $\\gamma^{s_{\\ell+1}}/(1-\\gamma)$, which diverges as $\\gamma \\to 1$, so the fixed exploration penalty no longer outweighs manipulation and the near-truthful equilibrium is not established.","fun_headline_variants_meta":{"raw":{"variants":["Near-optimal regret even when agents lie","Strategic agents cost nothing in online allocation","Lying agents can't sacrifice efficiency in this online mechanism","Incentive-aware online allocation hits non-strategic bound","Mechanism matches lower bound despite strategic reports"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001181,"raw_usage":{"total_tokens":4936,"prompt_tokens":1062,"completion_tokens":3874,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":678,"completion_tokens_details":{"reasoning_tokens":3801}},"tokens_in":678,"tokens_out":3874,"duration_ms":28759,"temperature":1.0,"reasoning_tokens":3801,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T17:58:22.429618+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the mechanism with nearly patient agents ($\\gamma = 1$ or $\\gamma = 1 - 1/T$), let them learn their reports with a high-capacity algorithm over thousands of repetitions, and measure whether large misreports persist and whether the average regret stays at $\\widetilde{O}(\\sqrt{T})$. A sharper targeted check comes from the paper's own Lemma B.3: in the two-agent identical-value example of Example 4, evaluate the inequality that must hold between the exploration loss ($1/(2K|E_\\ell|^3)$) and the discounted manipulation benefit; the regime where $\\gamma^{s_{\\ell+1}}/(1-\\gamma)$ exceeds that loss is precisely where the paper's proof no longer guarantees near-truthfulness.","supporting_citations":[{"cited_title":"The best of many worlds:: Dual mirror descent for online allocation problems","cited_arxiv_id":null,"evidence_quote":"The non-strategic primal-dual baseline whose Algorithm 1 is the vulnerable benchmark and whose regret framework the paper extends to strategic agents."},{"cited_title":"Incentive-aware contextual pricing with non-parametric market noise","cited_arxiv_id":null,"evidence_quote":"Supplies the $\\gamma$-impatient agent model (Assumption 1) and the inter-epoch manipulation-bounding technique used in Lemma B.3."},{"cited_title":"Online learning with predictable sequences","cited_arxiv_id":null,"evidence_quote":"Provides the Optimistic FTRL template that O-FTRL-FP extends to decision-dependent predictions."},{"cited_title":"Bandits with switching costs: T 2/3 regret","cited_arxiv_id":null,"evidence_quote":"Gives the low-switching hardness (Theorem 4.4) that forces the $\\Omega(T^{2/3})$ barrier for plain FTRL and motivates the optimistic fixed-point design."},{"cited_title":"Online allocation and learning in the presence of strategic agents","cited_arxiv_id":null,"evidence_quote":"Prior work on strategic agents in online allocation with homogeneous agents and fair-share constraints, which this paper generalizes."},{"cited_title":"Return of the bias: Almost minimax optimal high probability bounds for adversarial linear bandits","cited_arxiv_id":null,"evidence_quote":"The FTRL-FB idea of predicting through fixed points, adapted here to discontinuous argmax-based predictions."}],"review_version":1}