Single-Item Auctions with a Monopolist Intermediary

Aviad Rubinstein; Ertem Nusret Tas; Jingyi Liu; Qianfan Zhang; S. Matthew Weinberg

arxiv: 2605.21934 · v1 · pith:6WWUSZRQnew · submitted 2026-05-21 · 💻 cs.GT

Single-Item Auctions with a Monopolist Intermediary

Jingyi Liu , Aviad Rubinstein , Ertem Nusret Tas , S. Matthew Weinberg , Qianfan Zhang This is my paper

Pith reviewed 2026-05-22 02:57 UTC · model grok-4.3

classification 💻 cs.GT

keywords single-item auctionsmonopolist intermediaryregular distributionsstrongly regular distributionsposted pricesMyerson auctiontiming modelsmechanism design

0 comments

The pith

A monopolist intermediary can make the seller's revenue arbitrarily small relative to the direct-auction optimum for regular distributions.

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

This paper studies single-item auctions in which a revenue-maximizing intermediary controls which bids reach the seller. It compares outcomes across seller-first, intermediary-first, and simultaneous timing models. The analysis shows that when the seller moves first, deterministic mechanisms reduce to posted prices and the intermediary runs a shifted Myerson auction. This leads to a separation result: regular distributions allow the intermediary to drive the seller's revenue arbitrarily close to zero, but alpha-strongly regular distributions let posted prices secure a constant fraction of the optimum. The work demonstrates that the order of moves affects revenues and that simultaneous choice can harm both parties substantially.

Core claim

When the seller commits first to a mechanism, any deterministic mechanism collapses to a posted price, after which the intermediary best-responds with a shifted Myerson auction. For regular distributions this can make the seller's revenue arbitrarily small compared with the no-intermediary benchmark, whereas for alpha-strongly regular distributions posted prices recover a constant fraction whose dependence on alpha is tight. Timing between the two parties is consequential: neither sequential order dominates the other, and simultaneous play can leave both unboundedly worse off than either sequential regime.

What carries the argument

The reduction of the seller's deterministic mechanisms to posted prices under seller-first timing, together with the intermediary's shifted Myerson auction response.

If this is right

The seller obtains at best a posted-price mechanism when committing first against a strategic intermediary.
Posted prices achieve an approximation ratio that depends tightly on the strong-regularity parameter alpha.
Sequential timing yields better revenue guarantees for at least one party than simultaneous mechanism selection.
The results apply directly to intermediated markets such as blockchain transaction auctions and online advertising platforms.

Where Pith is reading between the lines

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

If sellers anticipate intermediaries, they may prefer to use posted prices even when more complex mechanisms would be optimal without an intermediary.
These timing effects might generalize to settings with multiple items or multiple competing intermediaries.
Regulators of intermediated markets could consider mandating sequential commitment orders to protect seller revenue.
Empirical studies on real auction platforms could test whether observed mechanisms align with the predicted collapse to posted prices.

Load-bearing premise

Bidders' values are drawn independently from a known distribution and the intermediary can choose which messages to forward to the seller.

What would settle it

Compute or simulate the seller's revenue when the intermediary is present versus absent, for a regular distribution such as uniform on [0,1] with two or more bidders; the ratio should approach zero as the number of bidders grows or parameters are tuned, while for an alpha-strongly regular distribution the ratio stays bounded away from zero by a function of alpha.

read the original abstract

Classical optimal auction theory assumes that bids reach the seller directly. We study how this picture changes when a revenue-maximizing intermediary controls access to the seller's auction. Motivated by blockchain auctions, online platforms, and other intermediated markets, we consider a single-item auction with independent private values and a monopolist intermediary who can decide which bidder messages are forwarded to the seller. We establish approximation guarantees and impossibility results across three timing models: seller-first, intermediary-first, and simultaneous. In the seller-first model, arbitrary deterministic seller mechanisms collapse to posted-price mechanisms, and the intermediary's best response is a shifted Myerson auction. This yields a sharp separation: for regular distributions, the seller's revenue can be arbitrarily small relative to the no-intermediary optimum, while for $\alpha$-strongly regular distributions, posted prices recover a constant fraction of the optimum with a tight dependence on $\alpha$. We further show that timing matters: neither Stackelberg order uniformly dominates, and simultaneous play can leave both parties unboundedly worse off than in either sequential model.

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.

Desk Editor's Note private letter to a colleague

The paper separates revenue outcomes by timing and regularity in intermediated auctions, with the seller-first collapse to posted prices driving the regular vs strongly regular split.

read the letter

The main thing to know is that this paper maps out how a monopolist intermediary who filters which bids reach the seller affects revenue, and that the order of moves plus the strength of regularity assumptions produce a sharp split in what the seller can achieve. In the seller-first model they show arbitrary deterministic seller mechanisms reduce to posted prices, which lets the intermediary's optimal response become a shifted Myerson auction. That produces the result that regular distributions can leave the seller with arbitrarily small revenue relative to the direct-auction benchmark, while alpha-strongly regular distributions let posted prices recover a constant fraction with tight alpha dependence. They also compare the three timing regimes and show neither sequential order dominates and simultaneous play can hurt both sides badly. These timing distinctions and the collapse step look new relative to classical optimal auction work. The models stay within standard independent private values, which keeps the analysis clean and the motivation from blockchain and platform settings is reasonable. The approximation and impossibility claims follow from the usual mechanism-design toolkit once the collapse is in place. The soft spot is exactly the one the stress-test flags: the collapse to posted prices carries a lot of weight for the separation. If some deterministic mechanisms have payment or allocation rules that depend on the forwarded message set in a non-trivial way and do not reduce cleanly, the subsequent revenue calculations would need adjustment. The abstract states the collapse without much elaboration, so the full proof needs checking to confirm it covers the whole class. The arbitrary-small-revenue construction for regular distributions also sits behind the abstract and would benefit from an explicit example. This is useful reading for people working on mechanism design with middlemen or on blockchain auction design. A reader who already knows Myerson and regularity conditions will get the most out of the timing comparisons and the regularity threshold. The questions are well-posed and the results organize a practical issue, so the paper deserves a serious referee even if some proofs need tightening.

Referee Report

2 major / 2 minor

Summary. This paper examines single-item auctions where a monopolist intermediary selectively forwards bidder messages to the seller, across three timing models: seller-first, intermediary-first, and simultaneous. In the seller-first model, arbitrary deterministic seller mechanisms are shown to collapse to posted-price mechanisms once the intermediary chooses which reports to forward; the intermediary's best response is then a shifted Myerson auction. This yields a sharp separation: for regular distributions the seller's revenue can be arbitrarily small relative to the no-intermediary optimum, while for α-strongly regular distributions posted prices recover a constant fraction of the optimum with tight dependence on α. The paper further shows that timing matters, with neither sequential order uniformly dominating the other and simultaneous play leaving both parties unboundedly worse off than in the sequential models.

Significance. If the collapse result and revenue bounds hold, the work contributes to mechanism design by incorporating a strategic intermediary, relevant to blockchain auctions and online platforms. The precise separation between regular and α-strongly regular distributions clarifies when intermediaries can erode seller revenue, and the timing analysis highlights the role of game structure. Strengths include the derivation from standard primitives (Myerson auction, regularity conditions) and the combination of approximation guarantees with impossibility results.

major comments (2)

[Abstract and seller-first model section] Abstract and seller-first model section: The claim that arbitrary deterministic seller mechanisms collapse to posted-price mechanisms (once the intermediary selects which messages to forward) is load-bearing for the entire revenue separation. It is stated without indicating whether the collapse holds for the full class of deterministic direct mechanisms (including those whose payment or allocation rules depend non-trivially on the set of forwarded reports) or only for mechanisms with fixed reserves. A complete proof or explicit verification for non-trivial payment rules is required to support both the arbitrarily-small revenue result for regular distributions and the constant-factor guarantee for α-strongly regular distributions.
[Revenue analysis for regular distributions] Revenue analysis for regular distributions: The construction demonstrating that seller revenue can be made arbitrarily small relies on the collapse. Explicit details on the family of regular distributions and the intermediary's forwarding strategy that achieves the separation should be supplied to permit verification of the impossibility claim.

minor comments (2)

[Notation and definitions] Clarify the precise definition of 'shifted Myerson auction' and its relation to the standard virtual-value maximizer when the intermediary controls the set of reports.
[Figures] If figures are used to depict the three timing models, ensure they explicitly label the sequence of moves and information sets.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. We address the two major points below and will revise the manuscript accordingly to strengthen the presentation of the collapse result and the impossibility construction.

read point-by-point responses

Referee: [Abstract and seller-first model section] Abstract and seller-first model section: The claim that arbitrary deterministic seller mechanisms collapse to posted-price mechanisms (once the intermediary selects which messages to forward) is load-bearing for the entire revenue separation. It is stated without indicating whether the collapse holds for the full class of deterministic direct mechanisms (including those whose payment or allocation rules depend non-trivially on the set of forwarded reports) or only for mechanisms with fixed reserves. A complete proof or explicit verification for non-trivial payment rules is required to support both the arbitrarily-small revenue result for regular distributions and the constant-factor guarantee for α-strongly regular distributions.

Authors: We thank the referee for highlighting the need for greater clarity on this foundational claim. The collapse result is intended to apply to the full class of deterministic direct mechanisms, including those whose payment or allocation rules may depend non-trivially on the set of forwarded reports. The argument shows that, once the intermediary chooses which reports to forward, the seller's mechanism is effectively reduced to a posted-price rule because the intermediary can always mimic the outcome of any more complex deterministic rule by its forwarding decision alone. We will add a complete, self-contained proof of the collapse (with explicit verification for mechanisms featuring non-trivial, set-dependent payment rules) to the seller-first model section in the revision. revision: yes
Referee: [Revenue analysis for regular distributions] Revenue analysis for regular distributions: The construction demonstrating that seller revenue can be made arbitrarily small relies on the collapse. Explicit details on the family of regular distributions and the intermediary's forwarding strategy that achieves the separation should be supplied to permit verification of the impossibility claim.

Authors: We agree that the impossibility construction would benefit from more explicit details. The separation for regular distributions is obtained via a parameterized family of regular distributions in which the intermediary's optimal forwarding strategy selectively forwards only low-virtual-value reports, inducing the seller to post a low price and thereby driving the seller's revenue to an arbitrarily small fraction of the no-intermediary optimum. We will supply the precise family of distributions, the closed-form description of the intermediary's forwarding rule, and the resulting revenue calculations in a dedicated subsection or appendix of the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation is self-contained from standard mechanism design

full rationale

The paper establishes its core results—including the collapse of arbitrary deterministic seller mechanisms to posted-price mechanisms in the seller-first timing model, the intermediary's best response as a shifted Myerson auction, and the revenue separation between regular and α-strongly regular distributions—through direct analysis of the three timing models and independent proofs. These steps rely on standard primitives of mechanism design (independent private values, Myerson's optimal auction) without reducing any central claim to a self-definition, a fitted parameter renamed as a prediction, or a load-bearing self-citation chain. The abstract and claimed theorems present the collapse and revenue bounds as derived outputs rather than inputs, and no equations or results are shown to be equivalent to their own assumptions by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper rests on standard domain assumptions from auction theory; no free parameters or invented entities are introduced in the abstract.

axioms (1)

domain assumption Bidders have independent private values
Explicitly stated in the abstract as the setting for the single-item auction.

pith-pipeline@v0.9.0 · 5724 in / 1180 out tokens · 33094 ms · 2026-05-22T02:57:22.197458+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

In the seller-first model, arbitrary deterministic seller mechanisms collapse to posted-price mechanisms, and the intermediary’s best response is a shifted Myerson auction. This yields a sharp separation: for regular distributions, the seller’s revenue can be arbitrarily small relative to the no-intermediary optimum, while for α-strongly regular distributions, posted prices recover a constant fraction of the optimum with a tight dependence on α.
IndisputableMonolith/Foundation/BranchSelection.lean branch_selection unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Theorem 2.3. Under Assumption 2.1, any deterministic mechanism Π_S that the seller uses is equivalent to a posted-price mechanism with price p=ω(Π_S)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

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Hartline and Tim Roughgarden , title =

Jason D. Hartline and Tim Roughgarden , title =

work page

[2] [2]

Myerson , title =

Roger B. Myerson , title =. Math. Oper. Res. , volume =

work page

[3] [3]

Ron Lavi and Or Sattath and Aviv Zohar , title =

work page

[4] [4]

An Incentive Analysis of Some Bitcoin Fee Designs (Invited Talk) , booktitle =

Andrew Chi. An Incentive Analysis of Some Bitcoin Fee Designs (Invited Talk) , booktitle =

work page

[5] [5]

Hao Chung and Elaine Shi , title =

work page

[6] [6]

The Review of Economic Studies , volume =

Huberman, Gur and Leshno, Jacob D and Moallemi, Ciamac , title = ". The Review of Economic Studies , volume =. 2021 , month =. doi:10.1093/restud/rdab014 , url =

work page doi:10.1093/restud/rdab014 2021

[7] [7]

Tim Roughgarden , title =

work page

[8] [8]

CoRR , volume =

Mallesh Pai and Max Resnick and Elijah Fox , title =. CoRR , volume =

work page

[9] [9]

Tarun Chitra and Matheus V. X. Ferreira and Kshitij Kulkarni , title =. CoRR , volume =

work page

[10] [10]

Mohammad Akbarpour and Shengwu Li , title =

work page

[11] [11]

Matheus V. X. Ferreira and S. Matthew Weinberg , title =

work page

[12] [12]

Meryem Essaidi and Matheus V. X. Ferreira and S. Matthew Weinberg , title =

work page

[13] [13]

Fabrice Benhamouda and Craig Gentry and Sergey Gorbunov and Shai Halevi and Hugo Krawczyk and Chengyu Lin and Tal Rabin and Leonid Reyzin , title =

work page

[14] [14]

Rivest, R. L. and Shamir, A. and Wagner, D. A. , title =. 1996 , publisher =

work page 1996

[15] [15]

and Conner, E

Buterin, V. and Conner, E. and Dudley, R. and Slipper, M. and Norden, I. and Bakhta, A. , year =

work page

[16] [16]

Michael ZhuScott Duke Kominers , year =

work page

[17] [17]

2023 , url =

The Evolution Of Ethereum MEV , author =. 2023 , url =

work page 2023

[18] [18]

Michael Zhu , year =

work page

[19] [19]

Jeffrey Burdges and Luca De Feo , title =

work page

[20] [20]

Hartline and Rad Niazadeh and Emmanouil Pountourakis and Yang Yuan , title =

Saeed Alaei and Jason D. Hartline and Rad Niazadeh and Emmanouil Pountourakis and Yang Yuan , title =. Games Econ. Behav. , volume =

work page

[21] [21]

Yaonan Jin and Pinyan Lu and Qi Qi and Zhihao Gavin Tang and Tao Xiao , title =

work page

[22] [22]

Scott Duke KominersTim Roughgarden , year =

work page

[23] [23]

CoRR , volume =

Jan Christoph Schlegel and Akaki Mamageishvili , title =. CoRR , volume =

work page

[24] [24]

CoRR , volume =

Vitalik Buterin and Virgil Griffith , title =. CoRR , volume =

work page

[25] [25]

Bitcoin-Enhanced Proof-of-Stake Security: Possibilities and Impossibilities , journal =

Ertem Nusret Tas and David Tse and Fisher Yu and Sreeram Kannan and Mohammad Ali Maddah. Bitcoin-Enhanced Proof-of-Stake Security: Possibilities and Impossibilities , journal =

work page

[26] [26]

Proceedings of the forty-sixth annual ACM symposium on Theory of computing , pages=

The sample complexity of revenue maximization , author=. Proceedings of the forty-sixth annual ACM symposium on Theory of computing , pages=

work page

[27] [27]

Mirrokni and S

Jon Feldman and Vahab S. Mirrokni and S. Muthukrishnan and Mallesh M. Pai , title =

work page

[28] [28]

Maryam Bahrani and Pranav Garimidi and Tim Roughgarden , title =

work page

[29] [29]

Moshe Babaioff and Moran Feldman and Moshe Tennenholtz , title =

work page

[30] [30]

Balseiro and Ozan Candogan , title =

Santiago R. Balseiro and Ozan Candogan , title =. Oper. Res. , volume =

work page

[31] [31]

13th Innovations in Theoretical Computer Science Conference (ITCS 2022) , year=

Maximizing Revenue in the Presence of Intermediaries , author=. 13th Innovations in Theoretical Computer Science Conference (ITCS 2022) , year=

work page 2022

[32] [32]

Stavrogiannis and Enrico H

Lampros C. Stavrogiannis and Enrico H. Gerding and Maria Polukarov , title =

work page

[33] [33]

Balseiro and Max Lin and Vahab S

Santiago R. Balseiro and Max Lin and Vahab S. Mirrokni and Renato Paes Leme and Song Zuo , title =

work page

[34] [34]

Doorenbos and Oren Etzioni and Daniel S

Robert B. Doorenbos and Oren Etzioni and Daniel S. Weld , title =. Agents , pages =

work page

[35] [35]

Kephart , title =

Amy Greenwald and Jeffrey O. Kephart , title =

work page

[36] [36]

NeurIPS , year =

Xiang Deng and Yu Gu and Boyuan Zheng and Shijie Chen and Samual Stevens and Boshi Wang and Huan Sun and Yu Su , title =. NeurIPS , year =

work page

[37] [37]

Xu and Hao Zhu and Xuhui Zhou and Robert Lo and Abishek Sridhar and Xianyi Cheng and Tianyue Ou and Yonatan Bisk and Daniel Fried and Uri Alon and Graham Neubig , title =

Shuyan Zhou and Frank F. Xu and Hao Zhu and Xuhui Zhou and Robert Lo and Abishek Sridhar and Xianyi Cheng and Tianyue Ou and Yonatan Bisk and Daniel Fried and Uri Alon and Graham Neubig , title =

work page

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2025 , url =

Emergence: Let a Billion APIs Compose , author =. 2025 , url =

work page 2025

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work page 2025

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Hugging Face , _author =

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Replicate , _author =

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