{"id":"c3ce6336-fe06-492e-96e0-650e3a300771","arxiv_id":"2505.17885","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":8.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"The paper introduces a game-theoretic model and the FPA-EQ fee mechanism for multi-proposer blockchains, with a tight 63.2% welfare guarantee and matching impossibility results.","lead":"This paper models how to set transaction fees in blockchains where many proposers build each block together, and proposes a first-price auction that splits all fees equally. It proves the mechanism resists proposer manipulation and keeps welfare within 63.2% of the optimum, and shows these tradeoffs are unavoidable.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Robustness of the 63.2% guarantee to non-IRR SPE is unestablished: Section 2.6 only exhibits a BP-subgame equilibrium, not a full SPE, and the paper neither proves bad SPEs exist nor shows they do not.","rationale":"The reader identified equilibrium selection as the weakest assumption, and I agree that is the most load-bearing issue for the central claim. However, the reader states that Section 2.6 provides subgame-perfect equilibria with welfare a constant factor below optimum; the paper only provides a BP-subgame Nash equilibrium with user bids fixed. A careful analysis of that example suggests the user side may undermine the bad BP equilibrium, so the existence of bad full SPEs is not settled. This makes the concern more precise: the paper needs either a proof that all SPEs (or at least all plausible equilibrium selections) achieve the 63.2% bound, or a concrete full-SPE counterexample. The other concerns raised by the reader (shill-cost accounting in Proposition 3.3, the unproved exchange argument for Corollary 3.11, and the terseness of Theorem 3.1's proof) are real but secondary; they do not directly threaten the conditional welfare theorem. Since the reader's conditional verdict already requires addressing proof gaps and clarifying the equilibrium-selection dependence, my concern does not move the verdict. I therefore recommend UNCHANGED, with the concrete test above serving to resolve whether the IRR restriction is essential.","tokens_in":19606,"tokens_out":46476,"duration_ms":355783,"concrete_test":"Perform a computational search over finite BP-asymmetric game structures (small m, k, overlapping sets S_j, and discrete valuation distributions), solving the FPA-EQ extensive-form game by backward induction with a discretized bid space to enumerate all subgame-perfect equilibria and their expected welfare. Include the Section 2.6 structure and check whether any SPE has welfare below (1-1/e) times the first-best. If such an SPE exists, the IRR qualification is essential; if exhaustive enumeration shows all SPEs attain at least 1-1/e, the qualification is unnecessary and the theorem can be strengthened.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Theorem 3.4's 1-1/e welfare bound is stated only for inclusion-rule-respecting subgame-perfect equilibria (IRR SPE). The paper motivates this restriction by saying other SPEs involve BPs 'inexplicably coordinating' on Pareto-dominated equilibria, and Section 2.6 gives a BP-subgame Nash equilibrium at bids (1,1) with welfare 0.5 of first-best. But that example fixes user bids and does not demonstrate a full SPE. In that structure, user 1 can deviate to a small positive bid below b2; the BP subgame then has a unique best-response outcome that includes both transactions, giving user 1 positive utility. Thus the existence of a non-IRR SPE with welfare below 1-1/e is not established. If such SPEs exist in some BP-asymmetric structure, the abstract's unconditional 'at equilibrium' claim is false. If they do not, the IRR restriction is vacuous and the theorem is stronger than stated. Either way, the central claim's robustness to equilibrium selection is unresolved, and this is the load-bearing issue for the paper's headline welfare guarantee.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper initiates the study of transaction fee mechanisms (TFMs) for leaderless blockchain protocols, where multiple block producers (BPs) contribute to each block. It proposes an extensive-form game model with users and BPs, defines a strong BP incentive-compatibility property (strongly BPIC), and introduces the FPA-EQ mechanism: the welfare-maximizing inclusion rule with a first-price payment rule and equal sharing of fees among BPs. The main results are that FPA-EQ is strongly BPIC, that every inclusion-rule-respecting (IRR) subgame-perfect equilibrium has expected welfare at least 1 - 1/e ~ 63.2% of the maximum, that this bound is tight, and that one cannot have strong BPIC together with DSIC or with exact optimal welfare. The analysis draws on smoothness-based price-of-anarchy bounds for matroid auctions.","tokens_in":19716,"tokens_out":19013,"duration_ms":149483,"significance":"If the results are correct, this is the first systematic treatment of TFM design for multi-proposer protocols, a setting of practical relevance given the deployment of DAG-based consensus protocols. The FPA-EQ mechanism is simple and its welfare guarantee is obtained through a clean reduction to winner-pays-bid matroid auctions, bringing modern price-of-anarchy tools into the TFM literature. The paper is also honest about the main caveat: the 63.2% guarantee is proved only for IRR SPE, i.e., equilibria in which BPs coordinate on the intended allocation in every subgame. Since that equilibrium-selection assumption is not microfounded, and since the abstract states the guarantee without the IRR qualifier, the practical significance of the headline bound depends on whether the qualifier can be removed or whether the abstract is revised. The impossibility results are useful context. Overall, the paper is a solid contribution to a timely topic, but the proof gaps identified below are load-bearing and need to be addressed.","major_comments":[{"comment":"The abstract states that FPA-EQ 'guarantees at least a 63.2% fraction of the maximum-possible expected welfare at equilibrium' without qualification. The body, however, only proves this for inclusion-rule-respecting SPE (Theorem 3.4). Corollary 3.11 asserts that in the BP-symmetric setting every SPE is IRR via 'a simple exchange argument,' but no argument is supplied. Thus the unqualified claim in the abstract is not supported. Moreover, Section 2.6 gives only a BP-subgame Nash equilibrium, not a full SPE, so the paper neither proves that non-IRR SPE with welfare below 63.2% exist nor rules them out. The authors should either prove Corollary 3.11, resolve the existence question for non-IRR SPE, and state the abstract precisely, or explicitly qualify all headline claims as applying to IRR SPE.","section":"Abstract; Section 3.3, Theorem 3.4 and Corollary 3.11"},{"comment":"The proof of Proposition 3.3 claims that every BP's payoff is proportional to the total amount paid by users (and hence to the sum of included bids). This ignores the definition in Section 2.1 that a BP's payoff is revenue from transactions other than its own minus payments it makes for shill transactions. Under FPA-EQ, if a BP includes its own shill transaction with bid s, it pays s but receives only s/m from the equal-share distribution, so its net payoff is not proportional to the sum of included bids. The proof must explicitly argue that shill inclusion is never strictly profitable for a deviating BP; as written, the derivation of strong BPIC is incomplete.","section":"Section 3.2, Proposition 3.3"},{"comment":"Lemma 3.6, which states that every IRR SPE of the FPA-EQ extensive-form game is user-outcome-equivalent to a Bayes-Nash equilibrium of a winner-pays-bid matroid auction, is the key step connecting the TFM game to the smoothness analysis. The proof is only a two-sentence sketch: it asserts that the IRR condition makes the induced allocation rule the welfare-maximizing matroid rule and that SPE conditions for users become BNE conditions. This is not immediate because the extensive-form game has sequential moves and information sets, so a formal argument is needed to show that unilateral deviations in the single-shot auction correspond exactly to deviations in the extensive-form game. Without a full proof of Lemma 3.6, Theorem 3.4 is not rigorously established.","section":"Section 3.3, Lemma 3.6"}],"minor_comments":[{"comment":"There are several typos: 'valaution' and 'TGM' in Lemma 3.6; 'winners-pay-bid' for 'winner-pays-bid' in the same paragraph; 'Fron' in the sentence after Proposition 3.5; 'insiting' in Section 3.1; and a missing phrase in Section 2.6: 'BPs that coordinate on the as demonstrated by Vickrey.'","section":"Throughout"},{"comment":"The statement of Theorem 3.2 says 'expected welfare strictly less than the minimum possible,' but the surrounding discussion makes clear that the intended wording is 'maximum possible.' Please correct this.","section":"Section 3.1, Theorem 3.2"},{"comment":"The application of Proposition A.4 in the proof of Lemma 3.10 is too terse. To verify the inequality sum_{i in A*} t_i(b_{-i}) <= sum_i p_i(b), the reader must infer that Proposition A.4 is applied with weights w=b, so that A* is the auction's winner set under b, and with the independent set A taken to be the welfare-optimal set under v. This should be spelled out explicitly.","section":"Section 3.3, Proof of Lemma 3.10"},{"comment":"The proof says 'A calculation shows' without showing the calculation. The expected-welfare computation is short and should be included so the tightness claim is directly verifiable.","section":"Section 3.3, Proposition 3.12"},{"comment":"The extensive-form model has users move sequentially but their information sets prevent them from observing earlier bids, effectively making the user stage simultaneous. This is a reasonable modeling choice, but it should be stated explicitly and justified, since readers may otherwise wonder why the order of user moves matters.","section":"Section 2.2"}],"recommendation":"major_revision","confidential_remarks":"The paper is well suited to the journal's scope and the core idea is promising. The main concern is that the abstract's unqualified welfare claim exceeds what is proved: Theorem 3.4 is restricted to IRR SPE, and the paper does not settle whether non-IRR SPE can have lower welfare or why such equilibria should be ignored. If the authors can prove Corollary 3.11, or alternatively adjust the abstract and add a substantive discussion of equilibrium selection, the paper could become acceptable. The shill-cost gap in Proposition 3.3 is likely fixable but must be addressed. I would not reject; the underlying results appear defensible, but the proof gaps are central."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should read this one. It starts a new subfield: transaction fee mechanisms for leaderless or multi-proposer protocols. The extensive-form model is sensible, the strong BPIC property is a genuinely useful definition, and FPA-EQ is an elegant mechanism—split every fee equally among all block producers, use the welfare-maximizing inclusion rule. The 1-1/e welfare bound via smoothness is a nice import of price-of-anarchy tools into TFM analysis, and the two impossibilities (no DSIC + strong BPIC with nontrivial welfare; no optimal welfare at equilibrium) plausibly delimit the design space. For a first paper in a new area, that is a solid contribution.\n\nThe soft spots are real but mostly addressable. The one that matters most is the equilibrium-selection issue. Theorem 3.4 only guarantees 63.2% for inclusion-rule-respecting subgame-perfect equilibria. The paper motivates this by saying other SPEs involve BPs inexplicably coordinating on Pareto-dominated equilibria, but it never shows such SPEs exist. The Section 2.6 example is not a full SPE—the user can deviate to a small positive bid and break the alleged bad equilibrium. So the abstract's unqualified \"at equilibrium\" overstates the result. Either prove that non-IRR SPE have decent welfare, or exhibit one with welfare below 1-1/e. Right now the scope of the headline theorem is unresolved.\n\nThe proof gaps are the usual referee-work items. Proposition 3.3's proof ignores the cost of shill transactions, which the model's own payoff definition includes. Lemma 3.6 (equivalence between IRR SPE and BNE of matroid auctions) is asserted more than proved. Corollary 3.11's \"simple exchange argument\" is absent. The application of Proposition A.4 inside Lemma 3.10 needs a careful statement—thresholds are defined in bid space while the revenue-covering lemma is stated for valuations. None of these looks fatal; they look like a promising paper that was rushed to release.\n\nWho gets value: anyone working on DAG-based consensus economics, TFM design, or multi-proposer mechanisms. It deserves a serious referee. Send it to peer review, and push the authors to tighten the proofs and settle the equilibrium-selection question. If they can do that, this is a strong paper.","headline":"New and important model for multi-proposer TFMs with a clean mechanism and a 1-1/e guarantee, but the equilibrium-selection caveat is bigger than the paper lets on and several proofs need real work.","tokens_in":20352,"tokens_out":4246,"would_cite":true,"duration_ms":51567,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["91B26","91A18","05B35"],"pacs":[],"model":"deepseek-v4-flash","headline":"Splitting transaction fees equally among all block producers makes the intended allocation a Pareto-dominant equilibrium and guarantees at least 63.2% of optimal welfare for leaderless blockchains.","keywords":["transaction fee mechanism","leaderless blockchain","DAG-based consensus","first-price auction with equal sharing","strong BPIC","subgame perfect equilibrium","price of anarchy","welfare approximation"],"falsifier":"To refute Theorem 3.4, exhibit a game structure, a valuation distribution, and an inclusion-rule-respecting subgame perfect equilibrium of FPA-EQ whose expected welfare is strictly below $(1 - 1/e)$ times the expected maximum; the tightness construction of Proposition 3.12 is the natural starting point. To refute Theorem 3.1, give a DSIC and strongly BPIC mechanism that nonetheless confirms transactions with positive probability on every positive valuation profile.","tokens_in":19308,"feed_emoji":"⛓️","tokens_out":7977,"duration_ms":86160,"temperature":0.7,"pith_summary":"The paper asks how a blockchain with many block producers, rather than a single leader, should charge and distribute transaction fees so that users and producers both behave well. It argues that a first-price auction in which every included transaction pays its bid and that payment is split equally among all block producers, called FPA-EQ, is strongly incentive-compatible for producers: the intended welfare-maximizing allocation is always a Nash equilibrium and Pareto dominates every other producer equilibrium. The paper proves that at any inclusion-rule-respecting subgame perfect equilibrium, expected welfare is at least $1 - 1/e \\approx 63.2\\%$ of the maximum possible, for arbitrary correlated user valuations, and that this bound is tight. It also proves that these compromises are unavoidable: no strongly producer-incentive-compatible mechanism with nontrivial welfare guarantees can be dominant-strategy truthful, and none can guarantee full efficiency. For the new generation of leaderless, DAG-based consensus protocols, this provides a concrete fee design with quantitative welfare guarantees.","feed_headline":"Equal sharing of fees yields a 63.2% welfare floor for leaderless chains","feed_subtitle":"A first-price auction that splits fees among all block producers keeps equilibrium welfare within 63 percent of the best possible.","key_machinery":"The central object is FPA-EQ, a transaction fee mechanism composed of a welfare-maximizing inclusion rule, a first-price confirmation and payment rule, and an equal-share distribution rule that gives every block producer $1/m$ of each included fee. The argument rests on two structural facts: feasible transaction sets form a matroid, so all welfare-maximizing allocations are equivalent and the intended allocation Pareto dominates all producer equilibria, establishing strong BPIC; and once producers are fixed to the intended allocation rule, the induced user game is a winner-pays-bid matroid auction, which is $(1 - 1/e, 1)$-smooth with private deviations. The smoothness price-of-anarchy theorem then converts this local deviation property into the global $63.2\\%$ welfare floor.","core_discovery":"The central claim is that FPA-EQ, built from the welfare-maximizing inclusion rule, the first-price payment rule, and equal sharing of each fee among all block producers, simultaneously solves the block-producer incentive problem and achieves near-optimal welfare in leaderless protocols. Theorem 3.4 states that for every game structure and every joint valuation distribution, every subgame perfect equilibrium in which block producers follow the intended Pareto-dominant allocation has expected welfare at least $1 - 1/e \\approx 63.2\\%$ of the first-best, and Proposition 3.12 gives a matching example, so the bound is tight. The proof first equates such equilibria with Bayes-Nash equilibria of winner-pays-bid matroid auctions, then uses the smoothness of those auctions to derive a price-of-anarchy bound. Corollaries extend the guarantee to all subgame perfect equilibria when block producers are symmetric, and to full efficiency when users are symmetric with i.i.d. valuations. The paper also shows the compromises are inherent: no strongly block-producer-incentive-compatible mechanism with nontrivial welfare guarantees can be dominant-strategy truthful for users, and none can guarantee optimal welfare at equilibrium.","pith_inferences":["The FPA-EQ rule can be read as a refinement of the pro-rata fee sharing already used in some DAG-based protocols: splitting each fee equally per block contributed, rather than by stake, makes the intended inclusion rule an equilibrium with a quantitative welfare guarantee.","Because the smoothness proof works for correlated valuations, the $63.2\\%$ floor is prior-robust; a controlled auction experiment with correlated values could test whether the inclusion-rule-respecting equilibrium selection actually arises in practice.","An incomplete-information extension in which block producers do not know each other's feasible sets, which the paper explicitly leaves open, would determine whether the strong BPIC guarantee survives private information.","The same 'game within the game' modeling could be carried over to settings where producers also pursue maximal extractable value or censorship objectives, to check whether a similar welfare floor persists under broader producer preferences."],"forward_implications":["The FPA-EQ mechanism gives a concrete deployable fee rule for multi-proposer protocols: include bids to maximize total fees and split each fee equally among all block producers.","Every inclusion-rule-respecting equilibrium, even with arbitrarily correlated user valuations, achieves at least $63.2\\%$ of the maximum possible expected welfare, and no better constant is possible in the worst case.","When block producers are symmetric, the $63.2\\%$ floor holds for every subgame perfect equilibrium, not only those that explicitly respect the inclusion rule.","When both block producers are symmetric and user valuations are i.i.d., every subgame perfect equilibrium of FPA-EQ achieves the maximum possible expected welfare.","Any strongly BPIC mechanism with nontrivial welfare guarantees cannot be DSIC, and no strongly BPIC mechanism can guarantee optimal welfare, so the bidding shading and the $63.2\\%$ floor are unavoidable trade-offs in this design space."],"supporting_citations":[{"why":"Defines smooth auctions with private deviations and proves that smoothness implies a price-of-anarchy bound, the template for Lemma 3.10.","marker":"[22]"},{"why":"Provides the formal smoothness definition and the smoothness-implies-PoA theorem used as Theorem 3.9.","marker":"[30]"},{"why":"Supplies the revenue-covering analysis for matroid auctions that yields the $(1 - 1/e, 1)$-smoothness of Lemma 3.10.","marker":"[16]"},{"why":"Supplies the first-price auction smoothness analysis that Lemma 3.10 adapts to winner-pays-bid matroid auctions.","marker":"[38]"},{"why":"Provides the example of first-price auction inefficiency adapted into Proposition 3.12 to prove tightness of the $63.2\\%$ bound.","marker":"[37]"},{"why":"Provides the matroid theory facts, including lexicographic optimality and greedy optimality, behind Propositions A.3 and A.4 that support strong BPIC and smoothness.","marker":"[27]"},{"why":"Supplies the single-proposer transaction fee mechanism model that the paper's extensive-form multi-proposer model extends.","marker":"[29]"}],"fun_headline_variants":["First-price auction with equal fee splits guarantees 63.2% welfare on leaderless chains","Equal-share first-price auction proves 63.2% welfare bound for leaderless blockchains","63.2% welfare floor from fee-sharing auction in leaderless protocols","First-price fee split assures 63.2% of optimal welfare without leaders","Leaderless blockchains: equal fee sharing yields 63.2% welfare guarantee"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"For every user bid vector, block producers coordinate on the intended inclusion-rule-respecting and Pareto-dominant Nash equilibrium rather than some other subgame-perfect equilibrium; the paper does not model how this coordination happens.","fun_headline_variants_meta":{"raw":{"variants":["First-price auction with equal fee splits guarantees 63.2% welfare on leaderless chains","Equal-share first-price auction proves 63.2% welfare bound for leaderless blockchains","63.2% welfare floor from fee-sharing auction in leaderless protocols","First-price fee split assures 63.2% of optimal welfare without leaders","Leaderless blockchains: equal fee sharing yields 63.2% welfare guarantee"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001224,"raw_usage":{"total_tokens":5049,"prompt_tokens":981,"completion_tokens":4068,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":597,"completion_tokens_details":{"reasoning_tokens":3960}},"tokens_in":597,"tokens_out":4068,"duration_ms":24296,"temperature":1.0,"reasoning_tokens":3960,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T14:40:43.942628+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"To refute Theorem 3.4, exhibit a game structure, a valuation distribution, and an inclusion-rule-respecting subgame perfect equilibrium of FPA-EQ whose expected welfare is strictly below $(1 - 1/e)$ times the expected maximum; the tightness construction of Proposition 3.12 is the natural starting point. To refute Theorem 3.1, give a DSIC and strongly BPIC mechanism that nonetheless confirms transactions with positive probability on every positive valuation profile.","supporting_citations":[{"cited_title":"In: Proceedings of the 12th ACM Conference on Electronic Commerce","cited_arxiv_id":null,"evidence_quote":"Defines smooth auctions with private deviations and proves that smoothness implies a price-of-anarchy bound, the template for Lemma 3.10."},{"cited_title":"Journal of Artificial Intelligence Research59, 59–101 (2017)","cited_arxiv_id":null,"evidence_quote":"Provides the formal smoothness definition and the smoothness-implies-PoA theorem used as Theorem 3.9."},{"cited_title":"In: Proceedings of the 15th ACM conference on Economics and Computation","cited_arxiv_id":null,"evidence_quote":"Supplies the revenue-covering analysis for matroid auctions that yields the $(1 - 1/e, 1)$-smoothness of Lemma 3.10."},{"cited_title":"In: Proceedings of the 45th annual ACM Symposium on Theory of Computing","cited_arxiv_id":null,"evidence_quote":"Supplies the first-price auction smoothness analysis that Lemma 3.10 adapts to winner-pays-bid matroid auctions."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the example of first-price auction inefficiency adapted into Proposition 3.12 to prove tightness of the $63.2\\%$ bound."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the matroid theory facts, including lexicographic optimality and greedy optimality, behind Propositions A.3 and A.4 that support strong BPIC and smoothness."},{"cited_title":"Transaction Fee Mechanism Design","cited_arxiv_id":"2106.01340","evidence_quote":"Supplies the single-proposer transaction fee mechanism model that the paper's extensive-form multi-proposer model extends."}],"review_version":1}