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arxiv: 2606.06633 · v1 · pith:7R6P5UM7new · submitted 2026-06-04 · 💻 cs.GT

Competing Auctions in Intermediated Markets

Bruno Mazorra , Minghao Pan , Christoph Schlegel This is my paper

Pith reviewed 2026-06-27 22:54 UTC · model grok-4.3

classification 💻 cs.GT
keywords competing auctionsintermediated marketsauction unravelingsingle-homingfirst-price auctionsecond-price auctionlatency asymmetryEthereum relays
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The pith

Sealed second-price intermediary auctions fully unravel into a first-price principal auction under single-homing.

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

The paper examines how a seller chooses among parallel auction mechanisms, including those offered by intermediaries in settings like Ethereum block production. It finds that when the intermediary enforces single-homing, sealed-bid second-price intermediary auctions completely unravel into the seller conducting a sealed first-price auction directly. Open bidding intermediaries unravel only partially, collapsing to first-price under symmetric latency and directing fast bidders to the intermediary under asymmetric latency. The results also apply when single-homing cannot be enforced in multi-plexing environments, and they highlight potential issues with the credibility of sealed bidding channels due to leakage incentives.

Core claim

When the intermediary can enforce single-homing on its bidders, sealed-bid second-price intermediary auctions fully unravel into the sealed first-price principal auction; open bidding-format intermediaries unravel only partially, collapsing into first-price in equilibrium under symmetric latency and sorting fast bidders to the intermediary under asymmetric latency. Any last-look advantage is removed through the availability of a credible sealed bidding channel. These results extend to multi-plexing environments. The seller has an incentive to leak information in a first-price auction against two or more fast bidders but benefits from committing to no leakage.

What carries the argument

Unraveling of intermediary auctions into the principal first-price auction under single-homing enforcement, analyzed with symmetric and asymmetric latency.

If this is right

  • The overall market structure converges to sealed first-price auctions when a credible sealed channel is available.
  • Open intermediaries partially unravel based on latency conditions.
  • The seller optimally commits to not leaking bids if possible.
  • In-protocol bidding channels limit the scope for out-of-protocol intermediary auctions.

Where Pith is reading between the lines

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

  • Adding verifiable no-leakage commitments could enhance the effectiveness of first-price auctions in multi-bidder fast environments.
  • The unraveling may reduce the value of complex intermediary protocols in favor of simpler direct mechanisms.
  • Results could inform auction design in other intermediated markets with parallel options beyond blockchain.
  • Asymmetric latency might create persistent segmentation between fast and slow bidders.

Load-bearing premise

The intermediary can enforce single-homing on its bidders together with the modeling of symmetric versus asymmetric latency.

What would settle it

Empirical evidence of widespread multi-homing by bidders across direct and intermediary channels, or a game-theoretic calculation showing seller leakage in first-price auctions with multiple fast bidders.

Figures

Figures reproduced from arXiv: 2606.06633 by Bruno Mazorra, Christoph Schlegel, Minghao Pan.

Figure 1
Figure 1. Figure 1: Last look vs First-price auction game representation. [PITH_FULL_IMAGE:figures/full_fig_p017_1.png] view at source ↗
read the original abstract

We analyze competing auctions in intermediated markets, where a seller selects among parallel mechanisms for the sale of a single good, most prominently the relay-and-protocol architecture of proposer-builder separation in Ethereum. When the intermediary can enforce single-homing on its bidders, sealed-bid second-price intermediary auctions fully unravel into the sealed first-price principal auction; open bidding-format intermediaries unravel only partially, collapsing into first-price in equilibrium under symmetric latency and sorting fast bidders to the intermediary under asymmetric latency. Any last-look advantage is removed through the availability of a credible sealed bidding channel. These results extend to multi-plexing environments (no enforcement by the intermediary). While the unraveling result indicates that the availability of a sealed first-price bidding channel pushes the overall market to the same auction structure, the very assumption of the credibility of such channel is problematic, as the seller may have an incentive to leak information: a first-price auction is leakage-resistant in the presence of a single ``fast'' bidder but not against two or more. However, if the seller can credibly commit to not leak bids, it is optimal for them to do so. A main motivation is the forthcoming Glamsterdam update of Ethereum: our analysis suggests that the availability of an in-protocol (first-price) bidding channel severely limits the design space for out-of-protocol auctions by relays and other intermediaries.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The paper analyzes competing auctions in intermediated markets, with a focus on the relay-and-protocol architecture of proposer-builder separation in Ethereum. It claims that when the intermediary enforces single-homing, sealed-bid second-price intermediary auctions fully unravel into the sealed first-price principal auction. Open bidding-format intermediaries unravel only partially: they collapse into first-price in equilibrium under symmetric latency, and sort fast bidders to the intermediary under asymmetric latency. The results extend to multi-plexing environments without single-homing enforcement. The paper notes that any last-look advantage is removed by a credible sealed bidding channel, but flags a credibility problem for the sealed first-price channel because the seller may have an incentive to leak information (leakage-resistant with one fast bidder but not with two or more); if the seller can commit to no leakage, it is optimal to do so. The main motivation is the forthcoming Glamsterdam update of Ethereum, which the analysis suggests will severely limit the design space for out-of-protocol auctions.

Significance. If the results hold, the paper provides a useful equilibrium analysis of how the introduction of a sealed first-price principal channel constrains intermediary auction design in blockchain settings. The explicit conditioning of full unraveling on single-homing enforcement, the latency-based distinction for open formats, and the extension to multi-plexing environments are strengths. The discussion of leakage incentives and commitment adds practical nuance to the theoretical claims.

major comments (2)
  1. [Model and single-homing assumption] The full unraveling result for sealed-bid second-price intermediaries is load-bearing on the single-homing enforcement assumption (explicitly flagged in the abstract); the model section should derive how this enforcement is implemented and whether it survives in the Ethereum relay context without additional restrictions.
  2. [Open bidding formats and latency] The partial unraveling claim for open formats (collapse to first-price under symmetric latency; sorting under asymmetric latency) is central to the main result; the equilibrium derivation in the relevant results section must show explicitly how the latency parameters produce these outcomes rather than post-hoc restrictions.
minor comments (3)
  1. [Abstract / Introduction] The abstract states equilibrium outcomes without visible model equations or proof sketches; the introduction or model section should include a brief overview of the key assumptions and equilibrium concept used.
  2. [Extensions] The term 'multi-plexing environments' is introduced without definition; add a short clarification or reference in the extension paragraph.
  3. [Introduction] The Glamsterdam update is mentioned as motivation; a footnote or short paragraph citing the relevant Ethereum proposal would improve accessibility for readers outside the blockchain community.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and the recommendation of minor revision. The comments identify areas where the exposition of modeling assumptions and equilibrium derivations can be strengthened, and we address each point below.

read point-by-point responses

  1. Referee: [Model and single-homing assumption] The full unraveling result for sealed-bid second-price intermediaries is load-bearing on the single-homing enforcement assumption (explicitly flagged in the abstract); the model section should derive how this enforcement is implemented and whether it survives in the Ethereum relay context without additional restrictions.

    Authors: We agree that the single-homing enforcement assumption is load-bearing for the full unraveling result. The model section currently introduces it as a feasible action available to the intermediary. To address the comment, we will expand the model section with a short derivation of implementation mechanisms (e.g., registration or cryptographic commitments) in the Ethereum relay setting and the conditions under which enforcement may require supplementary restrictions. This will clarify the scope without altering the core results. revision: yes

  2. Referee: [Open bidding formats and latency] The partial unraveling claim for open formats (collapse to first-price under symmetric latency; sorting under asymmetric latency) is central to the main result; the equilibrium derivation in the relevant results section must show explicitly how the latency parameters produce these outcomes rather than post-hoc restrictions.

    Authors: We agree that the equilibrium derivation should make the role of latency parameters fully explicit. The current analysis incorporates latency into bidders' expected payoffs and participation decisions, which generate the collapse under symmetric latency and the sorting outcome under asymmetric latency. We will revise the relevant results section to present the equilibrium conditions with the latency parameters shown step-by-step, ensuring the outcomes are derived directly rather than stated after the fact. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper derives equilibrium outcomes in a game-theoretic model of competing sealed-bid and open auctions with intermediaries, conditioned explicitly on assumptions such as single-homing enforcement and latency symmetry. No fitted parameters, self-definitional normalizations, or load-bearing self-citations appear in the abstract or described claims; results follow directly from incentive analysis without reducing predictions to inputs by construction. The extension to multi-plexing environments is noted as a modeling variant rather than a circular renormalization. This is the standard case of an independent theoretical derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 0 invented entities

Analysis rests on standard rational-play and equilibrium assumptions plus domain-specific modeling choices about enforcement and latency; no free parameters or invented entities are indicated in the abstract.

axioms (3)
  • domain assumption Intermediary can enforce single-homing on its bidders
    Explicit precondition stated for the full-unraveling result.
  • domain assumption Latency is either symmetric or asymmetric across bidders
    Used to differentiate partial unraveling and bidder sorting outcomes.
  • standard math Bidders and seller play according to subgame-perfect Nash equilibrium
    Implicit in all equilibrium unraveling statements.

pith-pipeline@v0.9.1-grok · 5769 in / 1286 out tokens · 24498 ms · 2026-06-27T22:54:26.678776+00:00 · methodology

discussion (0)

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Reference graph

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