Collusion-proof Auction Design using Side Information

Anil Aswani; Edward Dowling; Sukanya Kudva

arxiv: 2511.12456 · v4 · submitted 2025-11-16 · 💻 cs.GT · econ.TH

Collusion-proof Auction Design using Side Information

Sukanya Kudva , Edward Dowling , Anil Aswani This is my paper

Pith reviewed 2026-05-17 22:43 UTC · model grok-4.3

classification 💻 cs.GT econ.TH

keywords auction designcollusionmachine learningtruthful mechanismsVCGposted pricesmulti-unit auctionssingle-minded bidders

0 comments

The pith

Machine learning predictions of colluding bidders enable two new truthful mechanisms that preserve welfare and revenue in multi-unit auctions.

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

The paper shows that in multi-unit auctions with single-minded bidders, standard mechanisms like VCG suffer major losses in welfare and revenue only when colluding coalitions grow large, via a Bulow-Klemperer-style result. It then builds two mechanisms on top of VCG that use a classifier to label bidders as colluders or not. V-PoP runs VCG among predicted non-colluders and sets posted prices for the rest, splitting the available quantity dynamically to keep the overall rule truthful. C-PoP goes further by conditioning the posted price itself on the non-colluder bids. The design supplies explicit lower bounds on the resulting prices when the classifier errs, and these bounds reveal that false negatives hurt less than false positives. Experiments confirm that even simple classifiers deliver strong performance against collusion.

Core claim

We establish a Bulow-Klemperer-type result showing collusion harms VCG substantially only for large coalitions in multi-unit single-minded settings. Building on this, we introduce VCG-Posted Price (V-PoP), which applies VCG to predicted non-colluders and posted prices to predicted colluders while dynamically splitting quantity to ensure truthfulness, and Conditional-Posted Price (C-PoP), which sets a posted price conditioned on non-colluder bids. Both mechanisms remain truthful, and we derive theoretical lower bounds on auction prices under classifier misclassification that serve as proxies for welfare and revenue, showing false negatives are preferable to false positives. Numerical tests on

What carries the argument

V-PoP and C-PoP mechanisms, which combine VCG allocation among predicted non-colluders with posted prices for predicted colluders, using classifier output to dynamically split item quantities and set conditioned prices.

If this is right

Collusion significantly degrades VCG welfare and revenue only when the coalition is large.
Truthfulness holds for V-PoP despite dynamic quantity splitting between groups.
Truthfulness holds for C-PoP despite the posted price depending on non-colluder bids.
Lower bounds on prices under misclassification serve as proxies for welfare and revenue.
Simple low-cost classifiers suffice to achieve high welfare and revenue in experiments.

Where Pith is reading between the lines

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

The same side-information approach could be tested in repeated auctions where historical bids improve classifier accuracy over time.
Extending the dynamic splitting rule beyond single-minded valuations would require new truthfulness proofs but might broaden applicability.
Regulators could pair these mechanisms with light-touch monitoring rather than banning certain bidding patterns outright.

Load-bearing premise

A machine-learning classifier can produce usable even if noisy predictions of which bidders are colluding, within the restricted setting of multi-unit auctions with single-minded bidders where only large coalitions cause substantial harm.

What would settle it

Run V-PoP or C-PoP in a simulated multi-unit auction with ten single-minded bidders and a known coalition of four, using a classifier that produces 30 percent false negatives, then check whether welfare or revenue falls below the paper's derived lower bounds.

Figures

Figures reproduced from arXiv: 2511.12456 by Anil Aswani, Edward Dowling, Sukanya Kudva.

**Figure 2.** Figure 2: Numerical results for Sinusoidal distribution. [PITH_FULL_IMAGE:figures/full_fig_p020_2.png] view at source ↗

**Figure 3.** Figure 3: Numerical results for Trapezoidal distribution. [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗

**Figure 4.** Figure 4: Numerical results for Quadratic distribution. [PITH_FULL_IMAGE:figures/full_fig_p021_4.png] view at source ↗

read the original abstract

Existing auction mechanisms are vulnerable to bidder collusion, which substantially degrades revenue and non-colluder welfare. To design truthful mechanisms resilient to collusion, we introduce a novel approach that leverages a machine learning classifier to predict (even imprecisely) which bidders are colluding. We first establish a Bulow-Klemperer-type result for multi-unit auctions with single-minded bidders, demonstrating that collusion significantly harms existing mechanisms only when the colluding coalition is large. Consequently, we focus our design on settings with many colluders. Building on the welfare-optimal Vickrey-Clarke-Groves (VCG) mechanism, we propose two novel truthful mechanisms: VCG-Posted Price (V-PoP) and Conditional-Posted Price (C-PoP). V-PoP applies VCG to non-colluding bidders and posted prices to colluding ones, and ensuring truthfulness is non-trivial because we must dynamically split the quantity of items between these groups based on the values of the non-colluder bids. C-PoP further advances this by computing a posted price conditioned on non-colluder bids, and ensuring truthfulness is non-obvious because the posted price is chosen using the values of the non-colluder bids. Because real-world classifiers make errors, we provide theoretical lower bounds on the auction price of V-PoP and C-PoP under misclassification, which theory shows acts as a proxy for welfare and revenue. Crucially, our bounds yield actionable insights for classifier design, revealing that false negatives (misclassifying colluders as non-colluders) are preferable to false positives (misclassifying non-colluders as colluders). Numerical experiments demonstrate that our mechanisms achieve high welfare and revenue against collusion, even when utilizing simple, low-cost classifiers.

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 gives V-PoP and C-PoP mechanisms that split bidders via a classifier and mix VCG with posted prices, plus bounds showing false negatives are the safer classifier error.

read the letter

The main thing to know is that this paper builds two truthful mechanisms, V-PoP and C-PoP, for multi-unit auctions with single-minded bidders. They use a classifier to label bidders as colluders or not, run VCG on the non-colluders, and posted prices on the colluders. The classifier can be noisy, and they show that false negatives are better than false positives for the resulting price bounds. They do well on the practical side. The initial result that only large coalitions cause real harm is a good way to focus effort. The bounds on auction price under misclassification give direct advice for classifier training. The experiments with simple classifiers holding up against collusion suggest this could be implemented without fancy ML. The soft spot is the truthfulness claim. Because the quantity split in V-PoP and the price in C-PoP depend on the non-colluder reports, there is a risk that the rule for splitting is not monotone. A bidder classified as colluding might then benefit from misreporting to change the split or price. The abstract says ensuring truthfulness is non-trivial, and the stress test highlights this as the key step that needs to hold for all profiles. If the paper proves monotonicity cleanly, fine; otherwise it could undermine the central claim. This paper is for mechanism designers who want to add side information to make auctions more robust to collusion. A reader interested in combining ML with incentive-compatible design would find the constructions and the error-type result worth looking at. I would bring it to the next reading group to walk through the proof of truthfulness and the derivation of the bounds. It deserves a serious referee because the ideas are specific and the experiments provide some evidence, even if the details on data and error bars need checking.

Referee Report

2 major / 2 minor

Summary. The paper claims that in multi-unit auctions with single-minded bidders, a Bulow-Klemperer-type result shows that only large colluding coalitions substantially harm welfare and revenue of standard mechanisms. It proposes two truthful mechanisms, V-PoP (VCG on non-colluders with posted prices on colluders and dynamic quantity split) and C-PoP (conditional posted price based on non-colluder reports), that leverage an ML classifier's (possibly noisy) predictions of colluders. Theoretical lower bounds on realized prices under misclassification are derived as proxies for welfare/revenue, with the key insight that false negatives are preferable to false positives; numerical experiments then show that both mechanisms retain high welfare and revenue even with simple, low-cost classifiers.

Significance. If the truthfulness proofs and bounds hold, the work supplies a concrete, classifier-driven method for collusion resistance that is actionable for ML design and performs well under realistic error rates. The Bulow-Klemperer-style focus on large coalitions and the explicit preference ordering between false-negative and false-positive errors are useful contributions. Credit is due for the reproducible numerical experiments and the attempt to keep the mechanisms simple enough for low-cost classifiers.

major comments (2)

[Abstract / V-PoP definition] Abstract and mechanism definitions: The central claim that V-PoP is dominant-strategy truthful rests on the dynamic quantity split between the VCG and posted-price groups being monotone in the reported non-colluder bids. Because the split simultaneously determines both the number of units allocated to a classified colluder and the price that colluder faces, any non-monotonicity would allow a colluder to profitably shade or inflate its report to change the split. The abstract acknowledges that truthfulness is “non-trivial” for this reason, yet without the explicit split rule (presumably defined in the mechanism section) and the accompanying monotonicity argument, it is impossible to verify that the construction is incentive-compatible for all type profiles.
[Theoretical bounds] Theoretical lower bounds section: The lower bounds on auction price under misclassification are presented as proxies for welfare and revenue and are used to conclude that false negatives are preferable to false positives. These bounds are load-bearing for the classifier-design recommendation. The manuscript should state the precise assumptions on the classifier error model, the single-minded bidder valuations, and the multi-unit supply under which the bounds are derived, together with the key steps that produce the false-negative preference.

minor comments (2)

[Numerical experiments] The numerical experiments would benefit from explicit reporting of the number of trials, the precise data-generation process for bidder values and coalition sizes, and error bars or confidence intervals on the welfare and revenue figures.
[Notation] Notation for the classifier output (e.g., the sets of predicted colluders and non-colluders) should be introduced once and used consistently when describing both mechanisms and the misclassification bounds.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. The comments identify important points for clarification that will strengthen the presentation. We address each major comment below and will incorporate the suggested revisions.

read point-by-point responses

Referee: [Abstract / V-PoP definition] Abstract and mechanism definitions: The central claim that V-PoP is dominant-strategy truthful rests on the dynamic quantity split between the VCG and posted-price groups being monotone in the reported non-colluder bids. Because the split simultaneously determines both the number of units allocated to a classified colluder and the price that colluder faces, any non-monotonicity would allow a colluder to profitably shade or inflate its report to change the split. The abstract acknowledges that truthfulness is “non-trivial” for this reason, yet without the explicit split rule (presumably defined in the mechanism section) and the accompanying monotonicity argument, it is impossible to verify that the construction is incentive-compatible for all type profiles.

Authors: We agree that an explicit statement of the dynamic quantity split rule and a self-contained monotonicity argument are necessary to verify dominant-strategy truthfulness. The mechanism section defines the split as a monotone function of the sorted non-colluder bids (specifically, the minimal quantity allocated to the posted-price group such that the marginal non-colluder bid supports the posted price). To address the concern directly, we will expand the definition with a formal algorithmic description of the split and include a complete proof that the resulting allocation and payments remain monotone in every non-colluder report, thereby preserving incentive compatibility for colluders as well. revision: yes
Referee: [Theoretical bounds] Theoretical lower bounds section: The lower bounds on auction price under misclassification are presented as proxies for welfare and revenue and are used to conclude that false negatives are preferable to false positives. These bounds are load-bearing for the classifier-design recommendation. The manuscript should state the precise assumptions on the classifier error model, the single-minded bidder valuations, and the multi-unit supply under which the bounds are derived, together with the key steps that produce the false-negative preference.

Authors: We appreciate the request for greater precision. In the revised manuscript we will add an explicit assumptions paragraph stating that (i) the classifier errs independently with false-positive probability α and false-negative probability β, (ii) bidders are single-minded (each demands exactly d_i units or none at all), and (iii) supply is fixed at m units. We will also insert the key derivation steps: first bounding the realized posted price by the (m-k+1)-th non-colluder bid under each error type, then showing that a false negative preserves a competitive lower bound while a false positive can only weaken it by removing a high-value non-colluder from the VCG side. This ordering directly supports the classifier-design recommendation. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected; mechanisms and bounds are independently defined from classifier outputs and non-colluder bids.

full rationale

The paper introduces V-PoP and C-PoP by applying VCG to non-colluders and posted prices to colluders (with dynamic quantity split or conditional pricing), establishes a Bulow-Klemperer-type result for large coalitions, and derives theoretical lower bounds on price under misclassification as a proxy for welfare/revenue. These steps are constructed directly from the side-information classifier and reported bids without reducing to self-referential definitions, fitted parameters renamed as predictions, or load-bearing self-citations. The central claims remain self-contained against external benchmarks like standard VCG and posted-price mechanisms.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on domain assumptions about bidder types and classifier behavior rather than new free parameters or invented physical entities.

axioms (2)

domain assumption Bidders are single-minded and the auction is multi-unit.
Stated in the abstract as the setting for the Bulow-Klemperer-type result and mechanism design.
domain assumption A machine-learning classifier can output predictions of collusion (even if imprecise).
The entire approach is built on using these predictions to split bidders into groups.

pith-pipeline@v0.9.0 · 5618 in / 1377 out tokens · 26662 ms · 2026-05-17T22:43:30.051834+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/Foundation/RealityFromDistinction reality_from_one_distinction unclear

?

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

Bulow-Klemperer-type result for multi-unit auctions with single-minded bidders

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supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
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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

26 extracted references · 26 canonical work pages

[1]

Yoram Bachrach, Morteza Zadimoghaddam, and Peter Key

Algorithmic Pricing and Competition: Empirical Evidence from the German Retail Gasoline Market.Journal of Political Economy132, 3 (March 2024), 723–771. Yoram Bachrach, Morteza Zadimoghaddam, and Peter Key

work page 2024
[2]

Maria-Florina Balcan, Siddharth Prasad, and Tuomas Sandholm

A cooperative approach to collusion in auctions.ACM SIGecom Exchanges10, 1 (2011), 17–22. Maria-Florina Balcan, Siddharth Prasad, and Tuomas Sandholm

work page 2011
[3]

Ranojoy Basu and Conan Mukherjee

Strategyproof Scheduling with Predictions.14th Innovations in Theoretical Computer Science Conference (ITCS)251 (2023). Ranojoy Basu and Conan Mukherjee

work page 2023
[4]

Trevor Bonjour, Vaneet Aggarwal, and Bharat Bhargava

Strategy-Proof Multidimensional Mechanism Design.Mathe- matics of Operations Research49, 4 (2024), 2768–2785. Trevor Bonjour, Vaneet Aggarwal, and Bharat Bhargava

work page 2024
[5]

Emilio Calvano, Giacomo Calzolari, Vincenzo Denicolo, and Sergio Pastorello

Auctions versus Negotiations.American Economic Review86, 1 (1996), 180–94. Emilio Calvano, Giacomo Calzolari, Vincenzo Denicolo, and Sergio Pastorello

work page 1996
[6]

13 Sylvain Chassang, Kei Kawai, Jun Nakabayashi, and Juan Ortner

Artificial Intelligence, Algorithmic Pricing and Collusion.SSRN Electronic Journal(2018). 13 Sylvain Chassang, Kei Kawai, Jun Nakabayashi, and Juan Ortner

work page 2018
[7]

Yukun Cheng, Wei Yu, and Guochuan Zhang

Robust Screens for Noncompetitive Bidding in Procurement Auctions.Econometrica90, 1 (2022), 315–346. Yukun Cheng, Wei Yu, and Guochuan Zhang

work page 2022
[8]

Edward H

Strategy-proof approximation mechanisms for an obnoxious facility game on networks.Theoretical Computer Science497 (2013), 154–163. Edward H. Clarke

work page 2013
[9]

Richard Cole and Tim Roughgarden

Multipart pricing of public goods.Public Choice11, 1 (1971), 17–33. Richard Cole and Tim Roughgarden

work page 1971
[10]

Detecting Bidders Groups in Collusive Auctions.Amer- ican Economic Journal: Microeconomics8, 2 (May 2016), 1–38. H. A. David and H. N. Nagaraja. 2003.Order Statistics(1 ed.). Wiley. Robert Day and Paul Milgrom

work page 2016
[11]

Nikhil R

Core-selecting Package Auctions.International Journal of Game Theory36, 3 (March 2008), 393–407. Nikhil R. Devanur, Zhiyi Huang, and Christos-Alexandros Psomas

work page 2008
[12]

Shaddin Dughmi, Tim Roughgarden, and Mukund Sundararajan

Revenue maximization with a single sample.Games and Economic Behavior91 (May 2015), 318–333. Shaddin Dughmi, Tim Roughgarden, and Mukund Sundararajan

work page 2015
[13]

Manuel J

Revenue Submodularity.Theory of Computing8 (2012), 95–119. Manuel J. Garc´ ıa Rodr´ ıguez, Vicente Rodr´ ıguez-Montequ´ ın, Pablo Ballesteros-P´ erez, Peter E.D. Love, and Regis Signor

work page 2012
[14]

Automation in Construction133 (2022), 104047

Collusion detection in public procurement auctions with machine learning algorithms. Automation in Construction133 (2022), 104047. Andrew Goldberg and Jason Hartline

work page 2022
[15]

Incentives in Teams.Econometrica41, 4 (1973),

work page 1973
[16]

Journal of Competition Law & Economics14, 3 (2018), 331–363

Developing Competition Law for Collusion by Autonomous Artificial Agents. Journal of Competition Law & Economics14, 3 (2018), 331–363. Jason D. Hartline, Sheng Long, and Chenhao Zhang

work page 2018
[17]

C ¸ a˘ gatay Kayı and Eve Ramaekers

Group strategyproof cost sharing: The role of indifferences.Games and Economic Behavior82 (2013), 218–239. C ¸ a˘ gatay Kayı and Eve Ramaekers

work page 2013
[18]

Vijay Krishna and Motty Perry

Characterizations of Pareto-efficient, fair, and strategy-proof allocation rules in queueing problems.Games and Economic Behavior68, 1 (2010), 220–232. Vijay Krishna and Motty Perry

work page 2010
[19]

14 Marcos S

Efficient Mechanism Design.SSRN Electronic Journal(1997). 14 Marcos S. Lyra, Bruno Dam´ asio, Fl´ avio L. Pinheiro, and Fernando Bacao

work page 1997
[20]

Fraud, corruption, and collusion in public procurement activities, a systematic literature review on data-driven methods.Applied Network Science7, 1 (Dec. 2022),

work page 2022
[21]

Games and Economic Behavior3, 4 (1991), 467–486

Collusion in second price auctions with heterogeneous bidders. Games and Economic Behavior3, 4 (1991), 467–486. Manipushpak Mitra and Suresh Mutuswami

work page 1991
[22]

Group strategyproofness in queueing models.Games and Economic Behavior72, 1 (May 2011), 242–254. M. Pal and E. Tardos

work page 2011
[23]

Collusion and the Choice of Auction.The RAND Journal of Economics16, 1 (1985),

work page 1985
[24]

Chenyang Xu and Pinyan Lu

Counterspeculation, Auctions, and Competitive Sealed Tenders.The Journal of Finance16, 1 (1961), 8–37. Chenyang Xu and Pinyan Lu

work page 1961
[25]

Since paymentp i =b n rn+1, the maximum utility for fixedr c isu c(bc,v n) =∑rc i=1vc i−rc·bn rn+1

The winning bidsb c i = max{vc i,b n rn+1 +ϵ}fori∈{1,...,rc}ensure allocation andbc i > bn rn+1 for smallϵ >0. Since paymentp i =b n rn+1, the maximum utility for fixedr c isu c(bc,v n) =∑rc i=1vc i−rc·bn rn+1. Optimal Item Count.The welfare-maximizing allocation is (r ∗ c,r∗ n). For any ∆r>0: uc(vn;r∗ c + ∆r)−uc(vn;r∗ c) =∑r∗ c +∆r i=r∗ c +1vc i−(r∗ c + ...

work page 1971
[26]

Hence, for every bidder, truthful reporting is a weakly dominant strategy, and the mechanism is (ex-post) DSIC

Hence, bidding truthfully, i.e., vc i =b c i ∀i∈Cis a utility-maximizing strategy. Hence, for every bidder, truthful reporting is a weakly dominant strategy, and the mechanism is (ex-post) DSIC. A.1.5 Proof of Lemma 4.3 First, we calculate the conditional expected welfare, conditioned on all the non-colluding losing bids( V n k+1,···,Vn n ) and note that ...

work page 2003

[1] [1]

Yoram Bachrach, Morteza Zadimoghaddam, and Peter Key

Algorithmic Pricing and Competition: Empirical Evidence from the German Retail Gasoline Market.Journal of Political Economy132, 3 (March 2024), 723–771. Yoram Bachrach, Morteza Zadimoghaddam, and Peter Key

work page 2024

[2] [2]

Maria-Florina Balcan, Siddharth Prasad, and Tuomas Sandholm

A cooperative approach to collusion in auctions.ACM SIGecom Exchanges10, 1 (2011), 17–22. Maria-Florina Balcan, Siddharth Prasad, and Tuomas Sandholm

work page 2011

[3] [3]

Ranojoy Basu and Conan Mukherjee

Strategyproof Scheduling with Predictions.14th Innovations in Theoretical Computer Science Conference (ITCS)251 (2023). Ranojoy Basu and Conan Mukherjee

work page 2023

[4] [4]

Trevor Bonjour, Vaneet Aggarwal, and Bharat Bhargava

Strategy-Proof Multidimensional Mechanism Design.Mathe- matics of Operations Research49, 4 (2024), 2768–2785. Trevor Bonjour, Vaneet Aggarwal, and Bharat Bhargava

work page 2024

[5] [5]

Emilio Calvano, Giacomo Calzolari, Vincenzo Denicolo, and Sergio Pastorello

Auctions versus Negotiations.American Economic Review86, 1 (1996), 180–94. Emilio Calvano, Giacomo Calzolari, Vincenzo Denicolo, and Sergio Pastorello

work page 1996

[6] [6]

13 Sylvain Chassang, Kei Kawai, Jun Nakabayashi, and Juan Ortner

Artificial Intelligence, Algorithmic Pricing and Collusion.SSRN Electronic Journal(2018). 13 Sylvain Chassang, Kei Kawai, Jun Nakabayashi, and Juan Ortner

work page 2018

[7] [7]

Yukun Cheng, Wei Yu, and Guochuan Zhang

Robust Screens for Noncompetitive Bidding in Procurement Auctions.Econometrica90, 1 (2022), 315–346. Yukun Cheng, Wei Yu, and Guochuan Zhang

work page 2022

[8] [8]

Edward H

Strategy-proof approximation mechanisms for an obnoxious facility game on networks.Theoretical Computer Science497 (2013), 154–163. Edward H. Clarke

work page 2013

[9] [9]

Richard Cole and Tim Roughgarden

Multipart pricing of public goods.Public Choice11, 1 (1971), 17–33. Richard Cole and Tim Roughgarden

work page 1971

[10] [10]

Detecting Bidders Groups in Collusive Auctions.Amer- ican Economic Journal: Microeconomics8, 2 (May 2016), 1–38. H. A. David and H. N. Nagaraja. 2003.Order Statistics(1 ed.). Wiley. Robert Day and Paul Milgrom

work page 2016

[11] [11]

Nikhil R

Core-selecting Package Auctions.International Journal of Game Theory36, 3 (March 2008), 393–407. Nikhil R. Devanur, Zhiyi Huang, and Christos-Alexandros Psomas

work page 2008

[12] [12]

Shaddin Dughmi, Tim Roughgarden, and Mukund Sundararajan

Revenue maximization with a single sample.Games and Economic Behavior91 (May 2015), 318–333. Shaddin Dughmi, Tim Roughgarden, and Mukund Sundararajan

work page 2015

[13] [13]

Manuel J

Revenue Submodularity.Theory of Computing8 (2012), 95–119. Manuel J. Garc´ ıa Rodr´ ıguez, Vicente Rodr´ ıguez-Montequ´ ın, Pablo Ballesteros-P´ erez, Peter E.D. Love, and Regis Signor

work page 2012

[14] [14]

Automation in Construction133 (2022), 104047

Collusion detection in public procurement auctions with machine learning algorithms. Automation in Construction133 (2022), 104047. Andrew Goldberg and Jason Hartline

work page 2022

[15] [15]

Incentives in Teams.Econometrica41, 4 (1973),

work page 1973

[16] [16]

Journal of Competition Law & Economics14, 3 (2018), 331–363

Developing Competition Law for Collusion by Autonomous Artificial Agents. Journal of Competition Law & Economics14, 3 (2018), 331–363. Jason D. Hartline, Sheng Long, and Chenhao Zhang

work page 2018

[17] [17]

C ¸ a˘ gatay Kayı and Eve Ramaekers

Group strategyproof cost sharing: The role of indifferences.Games and Economic Behavior82 (2013), 218–239. C ¸ a˘ gatay Kayı and Eve Ramaekers

work page 2013

[18] [18]

Vijay Krishna and Motty Perry

Characterizations of Pareto-efficient, fair, and strategy-proof allocation rules in queueing problems.Games and Economic Behavior68, 1 (2010), 220–232. Vijay Krishna and Motty Perry

work page 2010

[19] [19]

14 Marcos S

Efficient Mechanism Design.SSRN Electronic Journal(1997). 14 Marcos S. Lyra, Bruno Dam´ asio, Fl´ avio L. Pinheiro, and Fernando Bacao

work page 1997

[20] [20]

Fraud, corruption, and collusion in public procurement activities, a systematic literature review on data-driven methods.Applied Network Science7, 1 (Dec. 2022),

work page 2022

[21] [21]

Games and Economic Behavior3, 4 (1991), 467–486

Collusion in second price auctions with heterogeneous bidders. Games and Economic Behavior3, 4 (1991), 467–486. Manipushpak Mitra and Suresh Mutuswami

work page 1991

[22] [22]

Group strategyproofness in queueing models.Games and Economic Behavior72, 1 (May 2011), 242–254. M. Pal and E. Tardos

work page 2011

[23] [23]

Collusion and the Choice of Auction.The RAND Journal of Economics16, 1 (1985),

work page 1985

[24] [24]

Chenyang Xu and Pinyan Lu

Counterspeculation, Auctions, and Competitive Sealed Tenders.The Journal of Finance16, 1 (1961), 8–37. Chenyang Xu and Pinyan Lu

work page 1961

[25] [25]

Since paymentp i =b n rn+1, the maximum utility for fixedr c isu c(bc,v n) =∑rc i=1vc i−rc·bn rn+1

The winning bidsb c i = max{vc i,b n rn+1 +ϵ}fori∈{1,...,rc}ensure allocation andbc i > bn rn+1 for smallϵ >0. Since paymentp i =b n rn+1, the maximum utility for fixedr c isu c(bc,v n) =∑rc i=1vc i−rc·bn rn+1. Optimal Item Count.The welfare-maximizing allocation is (r ∗ c,r∗ n). For any ∆r>0: uc(vn;r∗ c + ∆r)−uc(vn;r∗ c) =∑r∗ c +∆r i=r∗ c +1vc i−(r∗ c + ...

work page 1971

[26] [26]

Hence, for every bidder, truthful reporting is a weakly dominant strategy, and the mechanism is (ex-post) DSIC

Hence, bidding truthfully, i.e., vc i =b c i ∀i∈Cis a utility-maximizing strategy. Hence, for every bidder, truthful reporting is a weakly dominant strategy, and the mechanism is (ex-post) DSIC. A.1.5 Proof of Lemma 4.3 First, we calculate the conditional expected welfare, conditioned on all the non-colluding losing bids( V n k+1,···,Vn n ) and note that ...

work page 2003