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REVIEW 4 major objections 6 minor 67 references

ePBS lets proposers wait and reuse early bids, so builders shade and pool them, creating revenue and efficiency valleys that limited TEE commitment can partly reverse.

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2026-07-14 06:04 UTC pith:V7YSXAZ4

load-bearing objection Solid limited-commitment auction paper on ePBS: the ratchet is real and carefully proved; the ~25% TEE number is a best-found finite-grid illustration, not a certificate. the 4 major comments →

arxiv 2607.11240 v1 pith:V7YSXAZ4 submitted 2026-07-13 cs.GT econ.TH

From PBS to ePBS: the Microstructure of Block Building

Jingyu Liu , Bolin Zhang , Lin William Cong , Siguang Li , Xuechao Wang This is my paper
classification cs.GT econ.TH
keywords ePBSproposer-builder separationblock buildingratchet effectfirst-price auctionlimited commitmentTEE mechanism designlatency heterogeneity
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Ethereum is moving from relay-mediated proposer-builder separation (PBS) to enshrined ePBS, where builders bid directly to proposers and proposers choose when to stop and what bid history to reveal. The paper models both as versions of one two-stage auction in which an early bid is both a payment offer and a verifiable signal. Under PBS, exogenous stopping can still support separating first-price-like outcomes when stage-1 settlement is likely enough. Under ePBS, the proposer's ability to defer after seeing signed bids creates a ratchet: builders expect early information to be used against them later, so they shade or pool early bids. Exact equilibria in a simplified two-builder case and calibrated no-regret play on real builder values both show resulting revenue and allocation valleys. Full commitment would collapse to a static Myerson auction and remove the distortion; a TEE sidecar that commits only to stopping and disclosure recovers roughly a quarter more proposer revenue than the first-price benchmark in conservative finite designs.

Core claim

When the proposer can choose to defer after observing signed stage-1 bids and then use that history to intensify stage-2 competition, builders anticipate extraction and shade or pool early bids, producing allocation inefficiency and revenue-efficiency valleys relative to the first-price benchmark. Full commitment restores the static Myerson auction; limited TEE commitment to stopping and disclosure recovers about 25% more proposer revenue than first-price in the paper's finite benchmarks.

What carries the argument

The ratchet channel in the two-stage block-building game: an early signed bid is both a pay-as-bid offer and a verifiable signal the uncommitted ePBS proposer can exploit by deferring and disclosing, which induces uni-pooling perfect Bayesian equilibria (low types pool at zero, high types separate) and the same defensive pattern in calibrated no-regret play.

Load-bearing premise

The roughly 25% TEE revenue gain is a best-found result from a restricted nonconvex program on a small discrete bid-value grid, not a proven global optimum that is known to hold for continuous or larger markets.

What would settle it

On the paper's own calibrated Titan-BuilderNet game, if raising continuation reliability k2 through the intermediate range does not produce a joint drop in proposer revenue and allocation efficiency under no-regret play, or if a TEE-style committed stop-and-disclose policy fails to raise revenue above the first-price line by a material amount on that same grid, the central mechanism claim fails.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Relay-mediated PBS with exogenous stopping can retain first-price payoffs under separating equilibria when stage-1 settlement is sufficiently likely; ePBS does not automatically inherit that property.
  • ePBS compresses but does not eliminate fast-builder latency premia while adding a commitment-access gap that favors institutional proposers over solo validators.
  • A TEE sidecar that commits only to stopping and disclosure, without rewriting the native pay-as-bid rule, is a protocol-facing way to capture part of the full-commitment Myerson gain.
  • Protocol design that leaves stopping and disclosure fully ex post will induce defensive early pooling once continuation becomes credible.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If solo proposers cannot access TEEs or reputation, the ratchet may reintroduce centralization pressure even after relays are enshrined away.
  • The same stop-and-disclose ratchet logic would apply to other short-horizon auctions with verifiable early messages and optional continuation (for example, some MEV or batch-settlement designs).
  • A sharper continuous characterization of when latency premia survive endogenous disclosure would be the natural next theory step beyond the paper's simplified uni-pooling and finite TEE programs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper models Ethereum block building under PBS and ePBS as restrictions of a common imperfect-information two-stage auction with verifiable messages and latency-asymmetric information updates. PBS has exogenous stopping and full public disclosure; ePBS endogenizes stopping and disclosure after signed stage-1 bids, at the cost of lower canonicalization probability k2. Analytically, separating PBS PBEs preserve FPA interim payoffs when q1 is large enough (Lemma 1, Theorem 1) and are ruled out when q1 is too small (Proposition 4). In simplified two-fast-builder ePBS, the paper constructs a family of uni-pooling PBEs (Theorem 2) in which builders pool or shade early bids because the proposer can defer and exploit the bid history—a ratchet effect that can produce revenue and efficiency valleys relative to FPA. Full commitment collapses to static Myerson (Proposition 6). A TEE sidecar is proposed as limited commitment to stopping/disclosure while preserving pay-as-bid; the design is reduced to a bilinear/MI-QCQP program, and best-found solutions on a 5×5 grid raise proposer revenue by roughly 25% over FPA. Calibrated CFR+ (EFCCE) runs with Titan–BuilderNet values reproduce FPA-like PBS behavior and an ePBS revenue-efficiency valley.

Significance. If the qualitative results hold, the paper makes a clear contribution to blockchain market microstructure and limited-commitment auction design: it isolates how enshrining PBS shifts the proposer from a passive auctioneer to a sequential information designer, and it links that shift to a ratchet distortion rather than a pure latency race. The analytical PBS and simplified-ePBS characterizations are carefully scoped (regular pure class, regular bang-bang class, explicit cutoff admissibility CF(k2)), with full appendix proofs and envelope/rank-space arguments that are standard and checkable. The calibration is honestly labeled as approximate EFCCE rather than PBE and is grounded in relay traces, which strengthens external validity of the valley pattern. The TEE formulation as constrained information design under native pay-as-bid is a useful protocol-facing mitigation idea. The main significance risk is quantitative overclaim on the TEE gain: the ~25% figure is a best-found nonconvex finite-grid number under report-cap restrictions, not a certified optimum, so the mitigation half of the abstract is currently weaker than the ratchet diagnosis.

major comments (4)
  1. Abstract and §6.4 (also Theorem 3, Appendix G.5): The abstract states that the TEE design increases proposer revenue by approximately 25% relative to FPA. The body evaluates a report-capped, no-overbidding-domain computational program on a 5×5 value–bid grid and explicitly notes that the exact problem is a nonconvex MI-QCQP (NP-hard) and that reported numbers are best-found outcomes for a restricted benchmark, not certificates for the exact program. That gap is load-bearing for the mitigation half of the central claim. Either (i) strengthen the computation (larger grids, multiple starts with optimality gaps, or a tractable policy class with certified bounds) or (ii) rephrase the abstract and evaluation as a directional finite-grid illustration with the report-cap and non-global-optimality caveats stated up front.
  2. Definition 5 and Theorem 2 (Section 4.3): The uni-pooling ratchet is proved only in simplified ePBS, where the proposer may only stop or fully broadcast—no selective private disclosure. Full ePBS (Definition 2) and the calibrated game allow private/targeted disclosure, which is exactly the channel highlighted in Figure 8. The paper needs a tighter argument that the simplified construction is not an artifact of forbidding selective disclosure: either extend the analytical ratchet to a nontrivial selective-disclosure class, or give a formal reduction/robustness statement explaining why full-broadcast uni-pooling still identifies the same force that appears under private disclosure in §5.
  3. Section 6.1–6.2 and Figure 9: Proposition 6 shows full commitment implements static Myerson at stage 1, while the TEE is deliberately limited to stop/message commitment under native pay-as-bid. The institutional discussion notes that full Myerson may require a proxy that recreates relay-like intermediation—the problem ePBS was meant to reduce. The manuscript should make the welfare/centralization trade-off quantitative or at least sharper: under what conditions does limited TEE commitment dominate both uncommitted ePBS and proxy-Myerson once proxy concentration, liveness, and key-custody risks are counted, rather than treating TEE as an unambiguous leveling device.
  4. Section 5.1–5.2 and Appendix A: The calibrated valley is the main external-validity support for the ratchet outside the two-builder i.i.d. theory. CFR+ yields approximate EFCCE, which the paper correctly distinguishes from PBE, but the interpretation still treats stage-1 IR/BV declines and stop/disclose heatmaps as evidence of the same strategic channel as Theorem 2. Please add a short robustness check or diagnostic that the valley is not driven by coarse correlation alone (e.g., comparison to pure-strategy best-response dynamics, or restricted strategy spaces that force independent play), so the computational pattern can be read as corroboration rather than a weaker equilibrium class with different incentives.
minor comments (6)
  1. Figure 6–8 captions and §5.2: State units (mETH) and the exact latency profile labels consistently in every panel; some panels refer to Titan/BuilderNet while others use B1/B2 without a legend mapping.
  2. Proposition 3: The non-overbidding convention for stage-2 bids is introduced for the threshold claims but is not part of the baseline bid space in Section 3; flag this modeling choice earlier when the bid space is defined.
  3. Appendix B.1: The 100ms response-window censoring assumption for loser values is identifying; a one-paragraph sensitivity note (e.g., δ ∈ {50,100,200}ms) would help readers assess the joint log-normal fit.
  4. Notation: k⋆2(βFPA), CF(k2), and K+F appear in multiple sections; a short notation table would reduce cross-reference friction.
  5. Related work: Concurrent competing-auctions work [41] is discussed; a slightly sharper one-paragraph contrast on sealed FPA vs endogenous timing/disclosure would help position the contribution for non-specialists.
  6. Typos/consistency: “Respctively” in Figure 8 caption; occasional “Glamsterdam” roadmap dating; ensure arXiv subject and JEL codes match the final framing.

Circularity Check

0 steps flagged

No significant circularity: ratchet, Myerson collapse, and TEE gains are derived or computed from stated primitives, not forced by fitted inputs or self-citation.

full rationale

The paper’s load-bearing claims are self-contained. PBS payoff equivalence (Lemma 1) and separating existence/nonexistence (Thm 1, Prop 4) follow from standard envelope and rank-space first-price arguments under exogenous stopping; they are not defined in terms of the FPA benchmark they recover. The ePBS ratchet is an explicit PBE construction (Thm 2): uni-pooling bid schedules are pinned by local IC and cutoff admissibility C_F(k_2), then outcomes are computed from those equilibria—not fitted to produce valleys. Full commitment (Prop 6) applies Myerson’s envelope to discounted virtual surplus with k_1 ≥ k_2; the collapse to static Myerson is a standard implication, not a renamed empirical pattern. The ~25% TEE figure is the objective value of a stated (report-capped) finite program (Thm 3, §6.4), i.e., a best-found optimum of an optimization problem, not a parameter fitted to data and re-labeled as prediction. Calibration (§5, App. B) fits a joint log-normal to relay traces only to parameterize the CFR+ environment; theoretical claims do not depend on those fitted values. Citations are to external auction/information-design/CFR literature (Myerson, Bergemann–Morris, Skreta, Zinkevich et al.); there is no load-bearing self-citation uniqueness chain. Soft spots (nonconvex MI-QCQP, best-found not certified global) are correctness/robustness issues, not circularity.

Axiom & Free-Parameter Ledger

5 free parameters · 7 axioms · 2 invented entities

Load-bearing content is standard auction theory plus institutional modeling choices (two-stage abstraction, fast/slow RTT definition, pay-as-bid terminal rule, verifiable signed bids). Free parameters enter only the calibration and finite TEE grids, not the qualitative ratchet theorem. Invented entities are mechanism objects (TEE sidecar policy kernel), not physical postulates; independent evidence for TEEs exists outside the paper but the revenue number does not.

free parameters (5)
  • q1 (PBS exogenous stage-1 stop probability)
    Institutional free parameter swept in theory and calibration; existence/nonexistence thresholds depend on it.
  • k2 (ePBS delayed canonicalization probability)
    Reduced-form reliability of late proposal; calibrated from geo/latency maps; drives ratchet region and TEE comparisons.
  • Joint log-normal (μ, Σ) / common-value decomposition for Titan–BuilderNet
    Fitted by censored MLE on relay traces (blocks 23,000,151–24,698,991); defines the calibrated game prior FΔ.
  • Response window δ = 100ms for loser-bid censoring
    Hand-chosen identifying assumption for interval-censoring losing builder values.
  • Discretization (16 values × 31 bids for CFR; 5×5 grid for TEE)
    Computational free choices that shape reported EFCCE metrics and the ~25% TEE gain.
axioms (7)
  • domain assumption Terminal rule is highest-bid-wins pay-as-bid with symmetric tie-break; stage-2 bids weakly above stage-1 bids.
    Definitions 1–2 and eq. (1); native PBS/ePBS interface.
  • domain assumption Fast vs slow builders defined by whether P→B→P RTT allows conditioning on continuation messages before stage-2 stop.
    §3 and Fig 3; maps latency to information sets.
  • domain assumption k1 ≥ k2 with k1=1 in ePBS (costless within-slot waiting collapsed into stage 1).
    Definition 2; drives immediate-stop FPA region and Myerson stage-1 preference.
  • standard math IID regular values (Assumption 1) for analytical PBS/ePBS theorems; product prior F⊗n atomless with positive density.
    Used for Thm 1–2, Prop 4–5; standard Myerson/FPA regularity.
  • ad hoc to paper In simplified ePBS, proposer may only fully broadcast or stop—no selective private disclosure.
    Definition 5; tractability restriction for uni-pooling characterization.
  • standard math CFR+ empirical play approximates EFCCE, not exact PBE; used only as robustness check.
    §5 and App A; correctly scoped by authors.
  • domain assumption TEE enforces committed (ϕ,ψ)/kernel μ with native pay-as-bid terminal rule retained; no reserve/no-allocation without proxy.
    §6.2 Definition 8; limited-commitment scope of sidecar.
invented entities (2)
  • ePBS–TEE sidecar with direct information kernel μ independent evidence
    purpose: Limited public commitment device for stop and disclosure without rewriting pay-as-bid or requiring institutional proxy.
    Proposed mitigation; TEEs exist as hardware, but this policy kernel and revenue program are paper-specific.
  • Regular uni-pooling stage-1 rule with cutoff c and admissibility set CF(k2) no independent evidence
    purpose: Exact PBE family exhibiting the ratchet in simplified ePBS.
    Equilibrium construction, not an external object; independent evidence is the proof, not external measurement.

pith-pipeline@v1.1.0-grok45 · 65803 in / 4116 out tokens · 45989 ms · 2026-07-14T06:04:08.676123+00:00 · methodology

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read the original abstract

Ethereum's Glamsterdam upgrade introduces enshrined proposer-builder separation (ePBS), replacing relay-centric PBS with direct builder bids to proposers. We study how this shift changes the block-building microstructure through a general imperfect-information two-stage auction with verifiable messages, where an early bid serves as both a price offer and a signal. PBS and ePBS are modeled as restrictions of the same block-building game: PBS fixes stopping and disclosure exogenously, while ePBS lets the proposer choose stopping and disclosure ex post. Latency heterogeneity is captured by asymmetric information updates: fast builders observe disclosed early information before rebidding, while slow builders do not. We combine exact perfect Bayesian equilibrium characterizations in tractable cases with calibrated no-regret learning in finite games. For PBS, we show that separating equilibria preserve the standard first-price-auction payoff benchmark and provide conditions for their existence. For ePBS, we demonstrate a ratchet effect: because the proposer can defer block proposal and use early bid information in the second stage, builders anticipate ex-post extraction and shade or pool early bids, generating allocation inefficiency and revenue-efficiency valleys. We interpret this ratchet distortion as a commitment failure. Under full commitment, the optimal policy collapses to the static Myerson auction and removes the ratchet channel. To realize part of this commitment advantage in a feasible mechanism, we propose a Trusted Execution Environment (TEE) sidecar that enforces limited commitment. We formulate the revenue-maximizing TEE mechanism as a bilinear optimization problem. In conservative finite benchmarks, the TEE design increases the proposer revenue relative to the first-price benchmark by approximately \(25\%\).

Figures

Figures reproduced from arXiv: 2607.11240 by Bolin Zhang, Jingyu Liu, Lin William Cong, Siguang Li, Xuechao Wang.

Figure 1
Figure 1. Figure 1: Relay-mediated PBS and protocol-facing ePBS block-building flows. This tension is the central mechanism of the paper. Immediate proposal treats the winning bid as a first￾price payment offer, whereas deferred proposal turns early bids into verifiable signals that can influence later bidding. Thus, ePBS gives the proposer ex-post flexibility to wait and disclose strategically to induce higher bids, but only… view at source ↗
Figure 2
Figure 2. Figure 2: Winning-bid timing and proposing reliability. The left panel shows the empirical timing of winning MEV￾Boost PBS bids. The middle panel maps in-slot (adjusted) beacon block proposal time into proposer-region-specific block canonical probabilities. The right panel aligns canonicalization curves by the last no-loss block-proposal timing. Relay-Mediated PBS Block Auction. Ethereum’s current PBS implementation… view at source ↗
Figure 3
Figure 3. Figure 3: The block-building timeline. The upper curve maps proposal time to canonicalization probability, while the lower timeline shows communication within the block-building process. PBS and ePBS. We now derive PBS and ePBS as restrictions of the general block proposing game. In PBS, P is passive and the proposal timing and disclosure are relay-mediated and effectively exogenous; in ePBS, P is strategic. Empiric… view at source ↗
Figure 4
Figure 4. Figure 4: Uniform uni-pooling mechanism. Panel A plots the feasible nondegenerate cutoff correspondence c ∈ [c−(k2), c+(k2)] for k2 < 2/3 and the full-pooling range for k2 ≥ 2/3. Panel B shows the uni-pooling bid shape at k2 = .45. 0 1 2 2 3 1 0.1 0.12 0.14 0.16 0.18 k2 A. Builder payoff FPA B-best B-worst P -best P -worst 0 1 2 2 3 1 0.2 0.3 0.4 k2 B. Proposer revenue 0 1 2 2 3 1 0.7 0.8 0.9 1 k2 C. Efficiency [PI… view at source ↗
Figure 5
Figure 5. Figure 5: Uniform uni-pooling outcomes. Panels A–C plot the selection curves for builder payoff, proposer revenue, and efficiency from the same uniform family with respect to different k2; the gray bands mark the outcomes generated by feasible nondegenerate cutoff PBE, and the curves for k2 ≥ 2/3 are the full-pooling branch. Ratchet effect: a uniform example. For F(v) = v, K+ F = 2/3. Direct substitution in CF (k2) … view at source ↗
Figure 6
Figure 6. Figure 6: Computed no-regret outcome metrics for PBS and ePBS. The upper row reports PBS outcomes, and the lower row reports ePBS outcomes. From left to right, the columns show proposer revenue, B1’s utility, B2’s utility, and allocation efficiency. The computation is a calibrated no-regret benchmark, not an exact PBE computation. 1 mETH = 0.001 ETH [PITH_FULL_IMAGE:figures/full_fig_p020_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Stage-1 informativeness and bid shading in calibrated no-regret outcomes. The first two panels plot, for PBS as q1 varies, the information-reduction metric IRi←j and normalized bid-value ratio BVi . The last two panels plot the same diagnostics for ePBS as k2 varies. Higher IR means stage-1 bids are more separating, while lower BV means stronger bid shading. Dashed FPA curves give the pay-as-bid benchmark.… view at source ↗
Figure 8
Figure 8. Figure 8: ePBS behavior at k2 = 0.9 in the calibrated no-regret outcome. From left to right, panel 1 reports the stage-1 stop probability across the k2 sweep; panels 2 and 3 report the stage-1 bid distributions by value for Titan and BuilderNet; panels 4 and 5 report the proposer’s disclosure policy towards Titan and BuilderNet Respctively. For continuation histories, color denotes the probability that the recipient… view at source ↗
Figure 9
Figure 9. Figure 9: The real-world structure of full-commitment ePBS and ePBS-TEE implementation. In the TEE sidecar, the proposer need to import its block-proposal signing key and encodes its policy ex ante in the TEE-sidecar. mechanism therefore allocates immediately to the builder with the highest nonnegative virtual value and charges the corresponding Myerson payment. The proof is in Appendix G.1. Institutional full commi… view at source ↗
Figure 10
Figure 10. Figure 10: Best-found report-capped ePBS-TEE design. The panels show proposer revenue, builder utility, average stage-1 bids, and average on-path stage-1 stop probability as functions of k2. Performance [PITH_FULL_IMAGE:figures/full_fig_p030_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Validator mass and fast-builder exposure under the RTT(0.825) cutoff. Orange circles scale with validator count in the EF/RIG metadata. Stars mark the representative builder endpoints. Colored circles mark GCP proposer regions whose measured RTT to a representative endpoint is no larger than the regional cutoff implied by k2 = 0.825. These points identify where at least one representative endpoint can be … view at source ↗
Figure 12
Figure 12. Figure 12: reports a single 6 × 6 uniform-i.i.d. instance as k2 varies. Dark cells are low-stop, high￾continuation states, while yellow cells are states in which the TEE almost surely settles at stage 1. The low-stop region expands with k2, so continuation becomes more common without eliminating immediate settlement [PITH_FULL_IMAGE:figures/full_fig_p073_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: ePBS fast-fast behavior heatmap. The image is divided into two columns. Each column consists of three subfigures: the left panels show Titan’s stage-1 bid heatmap, the middle panels show BuilderNet’s stage-1 bid profile, and the right panels show the stage-1 proposal heatmap given observed stage-1 bid history. 75 [PITH_FULL_IMAGE:figures/full_fig_p075_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: ePBS slow-fast. Each row is one k2 value; within each row, the panels show Titan’s stage-1 bid profile, BuilderNet’s stage-1 bid profile, and the stage-1 stop profile. 76 [PITH_FULL_IMAGE:figures/full_fig_p076_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: ePBS fast-slow. Each row is one k2 value; within each row, the panels show Titan’s stage-1 bid profile, BuilderNet’s stage-1 bid profile, and the stage-1 stop profile. 77 [PITH_FULL_IMAGE:figures/full_fig_p077_15.png] view at source ↗

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