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arxiv: 2606.10169 · v1 · pith:CWH2AGRBnew · submitted 2026-06-08 · 💻 cs.GT

Benchmark-Tight Approximation Ratio of Simple Mechanism for a Unit-Demand Buyer

Yaonan Jin , Pinyan Lu This is my paper

Pith reviewed 2026-06-27 14:24 UTC · model grok-4.3

classification 💻 cs.GT
keywords revenue maximizationunit-demand buyeritem pricingapproximation ratioduality relaxation benchmarkprophet inequalitymechanism designsimple mechanisms
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The pith

Uniform-Ironed-Virtual-Value Item Pricing achieves a tight 3-approximation to the Duality Relaxation Benchmark for unit-demand buyers.

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

The paper establishes that a particular item pricing rule approximates optimal revenue within a factor of exactly 3 for one buyer who wants at most one item. It reaches this ratio by comparing the mechanism directly to the Duality Relaxation Benchmark rather than routing through Myerson Auction as an intermediate step. The proof rests on a new benchmark-based 3-competitive prophet inequality that is shown to be fully constructive. An impossibility result shows that the single-dimensional representative method cannot improve beyond 3 for many item pricings.

Core claim

Uniform-Ironed-Virtual-Value Item Pricing guarantees a tight 3-approximation to the Duality Relaxation Benchmark. All earlier analyses obtained only a 4-approximation because Uniform-Ironed-Virtual-Value Item Pricing is a tight 2-approximation to Myerson Auction and Myerson Auction is a tight 2-approximation to the benchmark; bypassing Myerson Auction removes one factor of 2. The new argument relies on a benchmark-based 3-competitive prophet inequality together with its constructive proof that directly yields the pricing rule.

What carries the argument

The benchmark-based 3-competitive prophet inequality whose constructive proof directly produces the Uniform-Ironed-Virtual-Value Item Pricing rule.

If this is right

  • The same pricing rule yields a revenue guarantee of 3 against the benchmark for any unit-demand instance.
  • The approach extends to other multi-item settings whose optimal revenue is relaxed to accessible benchmarks.
  • Any mechanism that follows the single-dimensional representative method cannot improve the ratio beyond 3 against the benchmark for a large class of item pricings.

Where Pith is reading between the lines

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

  • The constructive prophet inequality may be reusable in other mechanism-design problems that compare simple mechanisms to relaxation benchmarks.
  • Beating the ratio of 3 will require techniques that go beyond the single-dimensional representative approach.

Load-bearing premise

The benchmark-based 3-competitive prophet inequality holds and admits a fully constructive proof that directly supports the item pricing mechanism without intermediate steps.

What would settle it

A valuation distribution on which the revenue collected by Uniform-Ironed-Virtual-Value Item Pricing is strictly less than one-third the value of the Duality Relaxation Benchmark.

Figures

Figures reproduced from arXiv: 2606.10169 by Pinyan Lu, Yaonan Jin.

Figure 1
Figure 1. Figure 1: A diagram of the previous results and our new results. The four mechanisms constitute a [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Diagrams of revenue-quantile curves, virtual value CDF’s, and “ironing” [ [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Diagram of Case 3 in the proof of Lemma 2.6, in terms of revenue-quantile curves. ≤ max  φ(2)(v(2)), ve1, v(3), . . . , v(n)  = DRB(ve1, v−1) Case 2: ve1 ≻ v(2) ≻ v1. I.e., v1 is not the highest value in (v1, v−1) but ve1 is the highest value in (ve1, v−1). As mentioned in Section 2.1, an ironed virtual value is always upper bounded by the corresponding value φ(2)(v(2)) ≤ v(2). Thus for any choice of q1 … view at source ↗
Figure 4
Figure 4. Figure 4: The Iron reduction. (a) input non-concave revenue-quantile curves (b) output concave revenue-quantile curves (c) input badly-defined virtual value CDF’s (d) output well-defined virtual value CDF’s [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Diagrams of Iron with revenue-quantile curves and virtual value CDF’s. 16 [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The Truncate reduction. (a) input untruncated virtual value CDF’s (b) output truncated virtual value CDF’s (c) input untruncated revenue-quantile curves (d) output truncated revenue-quantile curves [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Diagrams of Truncate with virtual value CDF’s and revenue-quantile curves. 18 [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The Extend reduction. (a) input truncated revenue-quantile curves (b) output semi-linear revenue-quantile curves (c) input truncated virtual value CDF’s (d) output semi-linear virtual value CDF’s [PITH_FULL_IMAGE:figures/full_fig_p022_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Diagrams of Extend with virtual value CDF’s and revenue-quantile curves. 21 [PITH_FULL_IMAGE:figures/full_fig_p022_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: The Scale reduction. (a) input semi-linear revenue-quantile curves (b) output semi-linear revenue-quantile curves [PITH_FULL_IMAGE:figures/full_fig_p024_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Diagrams of Scale with revenue-quantile curves. 23 [PITH_FULL_IMAGE:figures/full_fig_p024_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: The Perturb reduction. (a) input semi-linear revenue-quantile curves (b) “positive” linear revenue-quantile curves (c) “negative” linear revenue-quantile curves [PITH_FULL_IMAGE:figures/full_fig_p027_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Diagrams of the Perturb reduction with revenue-quantile curves. 26 [PITH_FULL_IMAGE:figures/full_fig_p027_13.png] view at source ↗
read the original abstract

We study revenue maximization in the unit-demand single-buyer setting. Our main result is that \textsf{Uniform-Ironed-Virtual-Value Item Pricing} guarantees a {\em tight} $3$-approximation to the \textsf{Duality Relaxation Benchmark} [Chawla-Malec-Sivan, EC'10/GEB'15; Cai-Devanur-Weinberg, STOC'16/ SICOMP'21], breaking the barrier of $4$ since [Chawla-Hartline-Malec-Sivan, STOC'10; Chawla-Malec-Sivan, EC'10/GEB'15]. To our knowledge, this is the first {\em benchmark-tight} revenue guarantee of any simple multi-item mechanism. Technically, all previous works employ \textsf{Myerson Auction} as an intermediary. The barrier of $4$ follows as \textsf{Uniform-Ironed-Virtual-Value Item Pricing} achieves a {\em tight} $2$-approximation to \textsf{Myerson Auction}, which then achieves a {\em tight} $2$-approximation to \textsf{Duality Relaxation Benchmark}. Instead, our new approach avoids \textsf{Myerson Auction}, thus enabling the improvement. Central to our work are a {\em benchmark-based} $3$-competitive prophet inequality and its {\em fully constructive} proof. Such variant prophet inequalities shall find future applications, e.g., to Multi-Item Mechanism Design where optimal revenues are relaxed to various more accessible benchmarks. We complement our benchmark-tight ratio with an impossibility result. All previous works and ours follow the {\em single-dimensional representative} approach introduced by [Chawla-Hartline-Kleinberg, EC'07]. Against \textsf{Duality Relaxation Benchmark}, it turns out that this approach cannot beat our bound of $3$ for a large class of \textsf{Item Pricing}'s.

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

0 major / 3 minor

Summary. The paper claims that Uniform-Ironed-Virtual-Value Item Pricing achieves a tight 3-approximation to the Duality Relaxation Benchmark in the unit-demand single-buyer revenue maximization setting. This improves on the prior 4-approximation barrier by developing a benchmark-based 3-competitive prophet inequality with a fully constructive proof that directly yields the item pricing mechanism without routing through Myerson Auction as an intermediary. The paper also establishes an impossibility result showing that the single-dimensional representative approach cannot improve on 3 for a large class of item pricings against the benchmark.

Significance. If the central claim holds, the result is significant as the first benchmark-tight revenue guarantee achieved by any simple multi-item mechanism. The constructive benchmark-based prophet inequality is a strength that may enable future applications in multi-item mechanism design where revenues are relaxed to accessible benchmarks rather than optimal mechanisms.

minor comments (3)
  1. [Abstract and §1] The abstract and introduction could more explicitly contrast the new benchmark-based prophet inequality with prior prophet inequalities used in mechanism design to highlight the technical departure.
  2. [Impossibility section] In the impossibility result, the precise class of item pricings for which 3 cannot be beaten should be stated with a formal definition or reference to a specific theorem number.
  3. [§3] Notation for virtual values and ironing in the Uniform-Ironed-Virtual-Value Item Pricing definition would benefit from an inline example or diagram for clarity.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, significance assessment, and recommendation of minor revision. No specific major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity; derivation relies on independent prophet inequality proof

full rationale

The paper's central result derives the 3-approximation for Uniform-Ironed-Virtual-Value Item Pricing directly from a newly proved benchmark-based 3-competitive prophet inequality, without routing through Myerson Auction as an intermediary (which previously forced the 4-approximation via two successive 2-approximations). The abstract explicitly positions this prophet inequality and its constructive proof as the technical core, presented as a self-contained contribution rather than a fit, renaming, or self-citation reduction. No equations or steps in the provided description reduce the claimed guarantee to a tautology or prior self-citation chain; the impossibility result for single-dimensional representatives is consistent but does not create circularity. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work relies on standard assumptions from prior mechanism design literature on the duality relaxation benchmark and prophet inequalities; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • standard math Standard assumptions from prior works on duality relaxation benchmark and prophet inequalities
    The paper builds on results from Chawla et al. and Cai et al.

pith-pipeline@v0.9.1-grok · 5890 in / 1166 out tokens · 30545 ms · 2026-06-27T14:24:57.236803+00:00 · methodology

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Reference graph

Works this paper leans on

66 extracted references · 55 canonical work pages

  1. [1]

    John Thanassoulis , title =. J. Econ. Theory , volume =. 2004 , url =. doi:10.1016/j.jet.2003.09.002 , timestamp =

    work page doi:10.1016/j.jet.2003.09.002 2004

  2. [2]

    Hartline , editor =

    Nima Haghpanah and Jason D. Hartline , editor =. Reverse Mechanism Design , booktitle =. 2015 , url =. doi:10.1145/2764468.2764498 , timestamp =

    work page doi:10.1145/2764468.2764498 2015

  3. [3]

    Graham , title =

    Ronald L. Graham , title =. Inf. Process. Lett. , volume =. 1972 , url =. doi:10.1016/0020-0190(72)90045-2 , timestamp =

    work page doi:10.1016/0020-0190(72)90045-2 1972

  4. [4]

    On Revenue Monotonicity in Combinatorial Auctions , booktitle =

    Andrew Chi. On Revenue Monotonicity in Combinatorial Auctions , booktitle =. 2018 , url =. doi:10.1007/978-3-319-99660-8\_1 , timestamp =

    work page doi:10.1007/978-3-319-99660-8 2018

  5. [5]

    Book draft

    Mechanism design and approximation , author=. Book draft. October , volume=

  6. [6]

    Learning Reserve Prices in Second-Price Auctions , booktitle =

    Yaonan Jin and Pinyan Lu and Tao Xiao , editor =. Learning Reserve Prices in Second-Price Auctions , booktitle =. 2023 , url =. doi:10.4230/LIPIcs.ITCS.2023.75 , timestamp =

    work page doi:10.4230/lipics.itcs.2023.75 2023

  7. [7]

    2016 , isbn =

    Nikhil R. Devanur and Zhiyi Huang and Christos. The sample complexity of auctions with side information , booktitle =. 2016 , url =. doi:10.1145/2897518.2897553 , timestamp =

    work page doi:10.1145/2897518.2897553 2016

  8. [8]

    Matthew Weinberg , title =

    Patrick Briest and Shuchi Chawla and Robert Kleinberg and S. Matthew Weinberg , title =. J. Econ. Theory , volume =. 2015 , url =. doi:10.1016/j.jet.2014.04.011 , timestamp =

    work page doi:10.1016/j.jet.2014.04.011 2015

  9. [9]

    Sergiu Hart and Noam Nisan , title =. J. Econ. Theory , volume =. 2019 , url =. doi:10.1016/j.jet.2019.07.006 , timestamp =

    work page doi:10.1016/j.jet.2019.07.006 2019

  10. [10]

    Malec and Balasubramanian Sivan , title =

    Shuchi Chawla and David L. Malec and Balasubramanian Sivan , title =. Games Econ. Behav. , volume =. 2015 , url =. doi:10.1016/j.geb.2012.08.010 , timestamp =

    work page doi:10.1016/j.geb.2012.08.010 2015

  11. [11]

    Probability on Banach spaces , volume=

    On semiamarts, amarts, and processes with finite value , author=. Probability on Banach spaces , volume=. 1978 , publisher=

    1978

  12. [12]

    Sergiu Hart and Noam Nisan , title =. J. Econ. Theory , volume =. 2017 , url =. doi:10.1016/j.jet.2017.09.001 , timestamp =

    work page doi:10.1016/j.jet.2017.09.001 2017

  13. [13]

    Kleinberg and Tuomas Sandholm , title =

    Mohammad Taghi Hajiaghayi and Robert D. Kleinberg and Tuomas Sandholm , title =. Proceedings of the Twenty-Second. 2007 , url =

    2007

  14. [14]

    Theoretical Economics , volume=

    Maximal revenue with multiple goods: Nonmonotonicity and other observations , author=. Theoretical Economics , volume=. 2015 , publisher=

    2015

  15. [15]

    the Annals of Probability , pages=

    Comparison of threshold stop rules and maximum for independent nonnegative random variables , author=. the Annals of Probability , pages=. 1984 , publisher=

    1984

  16. [16]

    2022 , url =

    Yaonan Jin and Shunhua Jiang and Pinyan Lu and Hengjie Zhang , title =. 2022 , url =. doi:10.1137/21m1456364 , timestamp =

    work page doi:10.1137/21m1456364 2022

  17. [17]

    The Competition Complexity of Auctions:

    Alon Eden and Michal Feldman and Ophir Friedler and Inbal Talgam. The Competition Complexity of Auctions:. Proceedings of the 2017. 2017 , url =. doi:10.1145/3033274.3085115 , timestamp =

    work page doi:10.1145/3033274.3085115 2017

  18. [18]

    Matthew Weinberg , editor =

    Hedyeh Beyhaghi and S. Matthew Weinberg , editor =. Optimal (and benchmark-optimal) competition complexity for additive buyers over independent items , booktitle =. 2019 , url =. doi:10.1145/3313276.3316405 , timestamp =

    work page doi:10.1145/3313276.3316405 2019

  19. [19]

    On the Approximability of Simple Mechanisms for

    Yaonan Jin and Weian Li and Qi Qi , editor =. On the Approximability of Simple Mechanisms for. Web and Internet Economics - 15th International Conference,. 2019 , url =. doi:10.1007/978-3-030-35389-6\_17 , timestamp =

    work page doi:10.1007/978-3-030-35389-6 2019

  20. [20]

    2014 , timestamp =

    Vasileios Syrgkanis , title =. 2014 , timestamp =

    2014

  21. [21]

    Tight Bounds for the Price of Anarchy of Simultaneous First-Price Auctions , journal =

    George Christodoulou and Annam. Tight Bounds for the Price of Anarchy of Simultaneous First-Price Auctions , journal =. 2016 , url =. doi:10.1145/2847520 , timestamp =

    work page doi:10.1145/2847520 2016

  22. [22]

    Algorithmica , volume =

    George Christodoulou and Alkmini Sgouritsa and Bo Tang , title =. Algorithmica , volume =. 2018 , url =. doi:10.1007/s00453-017-0296-2 , timestamp =

    work page doi:10.1007/s00453-017-0296-2 2018

  23. [23]

    Theory Comput

    Georgios Birmpas and Evangelos Markakis and Orestis Telelis and Artem Tsikiridis , title =. Theory Comput. Syst. , volume =. 2019 , url =. doi:10.1007/s00224-018-9889-7 , timestamp =

    work page doi:10.1007/s00224-018-9889-7 2019

  24. [24]

    Games Econ

    Michal Feldman and Hu Fu and Nick Gravin and Brendan Lucier , title =. Games Econ. Behav. , volume =. 2020 , url =. doi:10.1016/j.geb.2015.11.009 , timestamp =

    work page doi:10.1016/j.geb.2015.11.009 2020

  25. [25]

    Composable and efficient mechanisms , booktitle =

    Vasilis Syrgkanis and. Composable and efficient mechanisms , booktitle =. 2013 , url =. doi:10.1145/2488608.2488635 , timestamp =

    work page doi:10.1145/2488608.2488635 2013

  26. [26]

    Benjamin Miller , editor =

    Shuchi Chawla and J. Benjamin Miller , editor =. Mechanism Design for Subadditive Agents via an Ex Ante Relaxation , booktitle =. 2016 , url =. doi:10.1145/2940716.2940756 , timestamp =

    work page doi:10.1145/2940716.2940756 2016

  27. [27]

    Mathematics of operations research , volume=

    Optimal auction design , author=. Mathematics of operations research , volume=. 1981 , publisher=

    1981

  28. [28]

    Yang Cai and Ziyun Chen and Jinzhao Wu , title =. 64th

  29. [29]

    Yaonan Jin and Pinyan Lu , title =. 63rd. 2022 , url =. doi:10.1109/FOCS54457.2022.00024 , timestamp =

    work page doi:10.1109/focs54457.2022.00024 2022

  30. [30]

    The Price of Stability for First Price Auction , booktitle =

    Yaonan Jin and Pinyan Lu , editor =. The Price of Stability for First Price Auction , booktitle =. 2023 , url =. doi:10.1137/1.9781611977554.ch14 , timestamp =

    work page doi:10.1137/1.9781611977554.ch14 2023

  31. [31]

    Near-linear Size Hypergraph Cut Sparsifiers , booktitle =

    Jason D. Hartline and Aleck C. Johnsen and Yingkai Li , editor =. Benchmark Design and Prior-independent Optimization , booktitle =. 2020 , url =. doi:10.1109/FOCS46700.2020.00036 , timestamp =

    work page doi:10.1109/focs46700.2020.00036 2020

  32. [32]

    Amine Allouah and Omar Besbes , title =. Manag. Sci. , volume =. 2020 , url =. doi:10.1287/mnsc.2019.3459 , timestamp =

    work page doi:10.1287/mnsc.2019.3459 2020

  33. [33]

    Optimal Pricing for

    Yiannis Giannakopoulos and Diogo Po. Optimal Pricing for. 2021 , url =. doi:10.1145/3434423 , timestamp =

    work page doi:10.1145/3434423 2021

  34. [34]

    and Childs, Andrew M

    Ning Chen and Nick Gravin and Pinyan Lu , editor =. Optimal competitive auctions , booktitle =. 2014 , url =. doi:10.1145/2591796.2591855 , timestamp =

    work page doi:10.1145/2591796.2591855 2014

  35. [35]

    Posted Price Mechanisms and Optimal Threshold Strategies for Random Arrivals , journal =

    Jos. Posted Price Mechanisms and Optimal Threshold Strategies for Random Arrivals , journal =. 2021 , url =. doi:10.1287/moor.2020.1105 , timestamp =

    work page doi:10.1287/moor.2020.1105 2021

  36. [36]

    Proceedings of the 55th Annual ACM Symposium on Theory of Computing , pages =

    Jos. A Constant Factor Prophet Inequality for Online Combinatorial Auctions , booktitle =. 2023 , url =. doi:10.1145/3564246.3585151 , timestamp =

    work page doi:10.1145/3564246.3585151 2023

  37. [37]

    Near-linear Size Hypergraph Cut Sparsifiers , booktitle =

    Paul D. An O(log log m) Prophet Inequality for Subadditive Combinatorial Auctions , booktitle =. 2020 , url =. doi:10.1109/FOCS46700.2020.00037 , timestamp =

    work page doi:10.1109/focs46700.2020.00037 2020

  38. [38]

    On the Computational Complexity of Optimal Simple Mechanisms , booktitle =

    Aviad Rubinstein , editor =. On the Computational Complexity of Optimal Simple Mechanisms , booktitle =. 2016 , url =. doi:10.1145/2840728.2840736 , timestamp =

    work page doi:10.1145/2840728.2840736 2016

  39. [39]

    The Complexity of Optimal Mechanism Design , booktitle =

    Constantinos Daskalakis and Alan Deckelbaum and Christos Tzamos , editor =. The Complexity of Optimal Mechanism Design , booktitle =. 2014 , url =. doi:10.1137/1.9781611973402.96 , timestamp =

    work page doi:10.1137/1.9781611973402.96 2014

  40. [40]

    On the Complexity of Simple and Optimal Deterministic Mechanisms for an Additive Buyer , booktitle =

    Xi Chen and George Matikas and Dimitris Paparas and Mihalis Yannakakis , editor =. On the Complexity of Simple and Optimal Deterministic Mechanisms for an Additive Buyer , booktitle =. 2018 , url =. doi:10.1137/1.9781611975031.133 , timestamp =

    work page doi:10.1137/1.9781611975031.133 2018

  41. [41]

    From pricing to prophets, and back! , journal =

    Jos. From pricing to prophets, and back! , journal =. 2019 , url =. doi:10.1016/j.orl.2018.11.010 , timestamp =

    work page doi:10.1016/j.orl.2018.11.010 2019

  42. [42]

    Matthew Weinberg , title =

    Aviad Rubinstein and S. Matthew Weinberg , title =. 2018 , url =. doi:10.1145/3105448 , timestamp =

    work page doi:10.1145/3105448 2018

  43. [43]

    Simple mechanisms for subadditive buyers via duality , booktitle =

    Yang Cai and Mingfei Zhao , editor =. Simple mechanisms for subadditive buyers via duality , booktitle =. 2017 , url =. doi:10.1145/3055399.3055465 , timestamp =

    work page doi:10.1145/3055399.3055465 2017

  44. [44]

    Hartline and Tim Roughgarden , editor =

    Jason D. Hartline and Tim Roughgarden , editor =. Simple versus optimal mechanisms , booktitle =. 2009 , url =. doi:10.1145/1566374.1566407 , timestamp =

    work page doi:10.1145/1566374.1566407 2009

  45. [45]

    Papadimitriou , editor =

    Yang Cai and Christos H. Papadimitriou , editor =. Simultaneous bayesian auctions and computational complexity , booktitle =. 2014 , url =. doi:10.1145/2600057.2602877 , timestamp =

    work page doi:10.1145/2600057.2602877 2014

  46. [46]

    On revenue maximization for selling multiple independently distributed items , journal =

    Xinye Li and Andrew Chi. On revenue maximization for selling multiple independently distributed items , journal =. 2013 , url =. doi:10.1073/pnas.1309533110 , timestamp =

    work page doi:10.1073/pnas.1309533110 2013

  47. [47]

    Andrew Chi. An. Proceedings of the Twenty-Sixth Annual. 2015 , url =. doi:10.1137/1.9781611973730.8 , timestamp =

    work page doi:10.1137/1.9781611973730.8 2015

  48. [48]

    Reaping the Benefits of Bundling under High Production Costs , booktitle =

    Will Ma and David Simchi. Reaping the Benefits of Bundling under High Production Costs , booktitle =. 2021 , url =

    2021

  49. [49]

    2022 , url =

    Constantinos Daskalakis and Maxwell Fishelson and Brendan Lucier and Vasilis Syrgkanis and Santhoshini Velusamy , title =. 2022 , url =. doi:10.1137/22m1471742 , timestamp =

    work page doi:10.1137/22m1471742 2022

  50. [50]

    Matthew Weinberg , title =

    Moshe Babaioff and Nicole Immorlica and Brendan Lucier and S. Matthew Weinberg , title =. J. 2020 , url =. doi:10.1145/3398745 , timestamp =

    work page doi:10.1145/3398745 2020

  51. [51]

    Computing simple mechanisms: Lift-and-round over marginal reduced forms , booktitle =

    Yang Cai and Argyris Oikonomou and Mingfei Zhao , editor =. Computing simple mechanisms: Lift-and-round over marginal reduced forms , booktitle =. 2022 , url =. doi:10.1145/3519935.3520029 , timestamp =

    work page doi:10.1145/3519935.3520029 2022

  52. [52]

    Yingkai Li , title =

  53. [53]

    Yaonan Jin and Pinyan Lu and Zhide Wei , title =

  54. [54]

    The menu-size complexity of auctions , booktitle =

    Sergiu Hart and Noam Nisan , editor =. The menu-size complexity of auctions , booktitle =. 2013 , url =. doi:10.1145/2492002.2482544 , timestamp =

    work page doi:10.1145/2492002.2482544 2013

  55. [55]

    Matthew Weinberg , title =

    Robert Kleinberg and S. Matthew Weinberg , title =. Games Econ. Behav. , volume =. 2019 , url =. doi:10.1016/j.geb.2014.11.002 , timestamp =

    work page doi:10.1016/j.geb.2014.11.002 2019

  56. [56]

    Games Econ

    Yang Cai and Constantinos Daskalakis , title =. Games Econ. Behav. , volume =. 2015 , url =. doi:10.1016/j.geb.2015.02.003 , timestamp =

    work page doi:10.1016/j.geb.2015.02.003 2015

  57. [57]

    Matthew Weinberg , editor =

    Pravesh Kothari and Sahil Singla and Divyarthi Mohan and Ariel Schvartzman and S. Matthew Weinberg , editor =. Approximation Schemes for a Unit-Demand Buyer with Independent Items via Symmetries , booktitle =. 2019 , url =. doi:10.1109/FOCS.2019.00023 , timestamp =

    work page doi:10.1109/focs.2019.00023 2019

  58. [58]

    Games Econ

    Xi Chen and Ilias Diakonikolas and Dimitris Paparas and Xiaorui Sun and Mihalis Yannakakis , title =. Games Econ. Behav. , volume =. 2018 , url =. doi:10.1016/j.geb.2018.03.016 , timestamp =

    work page doi:10.1016/j.geb.2018.03.016 2018

  59. [59]

    2020 , url =

    Yaonan Jin and Pinyan Lu and Zhihao Gavin Tang and Tao Xiao , title =. 2020 , url =. doi:10.1137/19M126178X , timestamp =

    work page doi:10.1137/19m126178x 2020

  60. [60]

    Hartline and David L

    Shuchi Chawla and Jason D. Hartline and David L. Malec and Balasubramanian Sivan , editor =. Multi-parameter mechanism design and sequential posted pricing , booktitle =. 2010 , url =. doi:10.1145/1806689.1806733 , timestamp =

    work page doi:10.1145/1806689.1806733 2010

  61. [61]

    Hartline and Robert D

    Shuchi Chawla and Jason D. Hartline and Robert D. Kleinberg , editor =. Algorithmic pricing via virtual valuations , booktitle =. 2007 , url =. doi:10.1145/1250910.1250946 , timestamp =

    work page doi:10.1145/1250910.1250946 2007

  62. [62]

    2022 , url =

    Xi Chen and Ilias Diakonikolas and Anthi Orfanou and Dimitris Paparas and Xiaorui Sun and Mihalis Yannakakis , title =. 2022 , url =. doi:10.1137/17m1136481 , timestamp =

    work page doi:10.1137/17m1136481 2022

  63. [63]

    Tight approximation ratio of anonymous pricing , booktitle =

    Yaonan Jin and Pinyan Lu and Qi Qi and Zhihao Gavin Tang and Tao Xiao , editor =. Tight approximation ratio of anonymous pricing , booktitle =. 2019 , url =. doi:10.1145/3313276.3316331 , timestamp =

    work page doi:10.1145/3313276.3316331 2019

  64. [64]

    Devanur and S

    Yang Cai and Nikhil R. Devanur and S. Matthew Weinberg , title =. 2021 , url =. doi:10.1137/16M1100113 , timestamp =

    work page doi:10.1137/16m1100113 2021

  65. [65]

    Matthew Weinberg , title =

    Yang Cai and Constantinos Daskalakis and S. Matthew Weinberg , title =. 53rd Annual. 2012 , url =. doi:10.1109/FOCS.2012.88 , timestamp =

    work page doi:10.1109/focs.2012.88 2012

  66. [66]

    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 =. 2019 , url =. doi:10.1016/j.geb.2018.08.003 , timestamp =

    work page doi:10.1016/j.geb.2018.08.003 2019