research-article

Sequential Posted-Price Mechanisms with Correlated Valuations

Authors:

Marek Adamczyk,

Diodato Ferraioli,

Bart De Keijzer,

Stefano LeonardiAuthors Info & Claims

ACM Transactions on Economics and Computation (TEAC), Volume 5, Issue 4

Article No.: 22, Pages 1 - 39

https://doi.org/10.1145/3157085

Published: 22 December 2017 Publication History

Abstract

We study the revenue performance of sequential posted-price mechanisms and some natural extensions for a setting where the valuations of the buyers are drawn from a correlated distribution. Sequential posted-price mechanisms are conceptually simple mechanisms that work by proposing a “take-it-or-leave-it” offer to each buyer. We apply sequential posted-price mechanisms to single-parameter multiunit settings in which each buyer demands only one item and the mechanism can assign the service to at most k of the buyers.

For standard sequential posted-price mechanisms, we prove that with the valuation distribution having finite support, no sequential posted-price mechanism can extract a constant fraction of the optimal expected revenue, even with unlimited supply. We extend this result to the case of a continuous valuation distribution when various standard assumptions hold simultaneously (i.e., everywhere-supported, continuous, symmetric, and normalized (conditional) distributions that satisfy regularity, the MHR condition, and affiliation). In fact, it turns out that the best fraction of the optimal revenue that is extractable by a sequential posted-price mechanism is proportional to the ratio of the highest and lowest possible valuation.

We prove that a simple generalization of these mechanisms achieves a better revenue performance; namely, if the sequential posted-price mechanism has for each buyer the option of either proposing an offer or asking the buyer for its valuation, then a Ω (1/max { 1,d}) fraction of the optimal revenue can be extracted, where d denotes the degree of dependence of the valuations, ranging from complete independence (d=0) to arbitrary dependence (d = n-1).

References

[1]

I. Abraham, S. Athey, M. Babaioff, and M. Grubb. 2013. Peaches, lemons, and cookies: Designing auction markets with dispersed information. In Proceedings of the 14th ACM Conference on Electronic Commerce. ACM, 7--8.

Digital Library

[2]

M. Adamczyk, A. Borodin, D. Ferraioli, B. de Keijzer, and S. Leonardi. 2015. Sequential posted price mechanisms with correlated valuations. In Proceedings of the 11th International Conference on Web and Internet Economics (WINE’15). Springer, 1--15.

Digital Library

[3]

M. Adamczyk, M. Sviridenko, and J. Ward. 2014. Submodular stochastic probing on matroids. In Proceedings of the 31st International Symposium on Theoretical Aspects of Computer Science (STACS’14). Schloss Dagstuhl, 29--40.

[4]

L. M. Ausubel. 1999. A Generalized Vickrey Auction. Technical Report. University of Maryland.

[5]

M. Babaioff, S. Dughmi, R. Kleinberg, and A. Slivkins. 2012. Dynamic pricing with limited supply. In Proceedings of the 13th ACM Conference on Economics and Computation (EC’12). ACM, 74--91.

Digital Library

[6]

M. Babaioff, N. Immorlica, and R. Kleinberg. 2007. Matroids, secretary problems, and online mechanisms. In Proceedings of the 18th ACM-SIAM Symposium on Discrete Algorithms (SODA’07). SIAM.

Digital Library

[7]

M. Babaioff, N. Immorlica, B. Lucier, and S. M. Weinberg. 2014. A simple and approximately optimal mechanism for an additive buyer. In Proceedings of the 55th Annual IEEE Symposium on Foundations of Computer Science (FOCS’14). IEEE, 21--30.

Digital Library

[8]

M. Babaioff, R. Kleinberg, and R. Paes Leme. 2012. Optimal mechanisms for selling information. In Proceedings of the 13th ACM Conference on Electronic Commerce. ACM, 92--109.

Digital Library

[9]

A. Blum and J. D. Hartline. 2005. Near-optimal online auctions. In Proceedings of the 16th ACM-SIAM Symposium on Discrete Algorithms (SODA’05). SIAM, 1156--1163.

Digital Library

[10]

A. Blum, V. Kumar, A. Rudra, and F. Wu. 2004. Online learning in online auctions. Theoretical Computer Science 324 (2004), 137--146.

Digital Library

[11]

L. Blumrosen and T. Holenstein. 2008. Posted prices vs. negotiations: An asymptotic analysis. In Proceedings of the 9th ACM Conference on Economics and Computation (EC’08). ACM, 49--49.

Digital Library

[12]

T. Börgers. 2015. An Introduction to the Theory of Mechanism Design. Oxford University Press.

[13]

S. Chawla, H. Fu, and A. Karlin. 2014. Approximate revenue maximization in interdependent value settings. In Proceedings of the 15th ACM Conference on Economics and Computation (EC’14). ACM, 277--294.

Digital Library

[14]

S. Chawla, J. D. Hartline, D. L. Malec, and B. Sivan. 2010. Multi-parameter mechanism design and sequential posted pricing. In Proceedings of the 42nd ACM Symposium on Theory of Computing (STOC’10). ACM, 311--320.

Digital Library

[15]

N. Chen, N. Immorlica, A. R. Karlin, M. Mahdian, and A. Rudra. 2009. Approximating matches made in heaven. In Proceedings of the 36th International Colloquium on Automata, Languages and Programming (ICALP’09). Springer, 266--278.

Digital Library

[16]

E. H. Clarke. 1971. Multipart pricing of public goods. Public Choice 11, 1 (1971), 17--33.

[17]

J. Cremer and R. P. McLean. 1988. Full extraction of the surplus in Bayesian and dominant strategy auctions. Econometrica 56, 6 (1988), 1247--1257.

[18]

N. R. Devanur, J. Morgenstern, V. Syrgkanis, and S. M. Weinberg. 2015. Simple auctions with simple strategies. In Proceedings of the 16th ACM Conference on Economics and Computation (EC’15). ACM, 305--322.

Digital Library

[19]

S. Dobzinski, H. Fu, and R. D. Kleinberg. 2011. Optimal auctions with correlated bidders are easy. In Proceedings of the 43rd ACM Symposium on Theory of Computing (STOC’11). ACM, 129--138.

Digital Library

[20]

R. El-Yaniv, A. Fiat, R. M. Karp, and G. Turpin. 2001. Optimal search and one-way trading online algorithms. Algorithmica 30, 1 (2001), 101--139.

[21]

M. Feldman, N. Gravin, and B. Lucier. 2015. Combinatorial auctions via posted prices. In Proceedings of the 26th ACM-SIAM Symposium on Discrete Algorithms (SODA’15). SIAM, 123--135.

Digital Library

[22]

M. Feldman, O. Svensson, and R. Zenklusen. 2016. Online contention resolution schemes. In Proceedings of the 27th ACM-SIAM Symposium on Discrete Algorithms. SIAM, 1014--1033.

Digital Library

[23]

T. Groves. 1973. Incentives in teams. Econometrica 14, 4 (1973), 617--631.

[24]

A. Gupta and V. Nagarajan. 2013. A stochastic probing problem with applications. In Proceedings of the 16th Conference on Integer Programming and Combinatorial Optimization (IPCO’13). Springer.

Digital Library

[25]

S. Hart and N. Nisan. 2012. Approximate revenue maximization with multiple items. In Proceedings of the 13th ACM Conference on Economics and Computation (EC’12). ACM, 656--656.

Digital Library

[26]

J. D. Hartline and T. Roughgarden. 2009. Simple versus optimal mechanisms. SIGecom Exchanges 8, 1 (2009), 5:1--5:3.

Digital Library

[27]

J. H. Kagel, R. M. Harstad, and D. Levin. 1987. Information impact and allocation rules in auctions with affiliated private values: A laboratory study. Econometrica 55, 6 (1987), 1275--1304.

[28]

R. Kleinberg and T. Leighton. 2003. The value of knowing a demand curve: Bounds on regret for online posted-price auctions. In Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science (FOCS’03). IEEE, 594--594.

Digital Library

[29]

R. Kleinberg and S. M. Weinberg. 2012. Matroid prophet inequalities. In Proceedings of the 44th ACM Symposium on Theory of Computing (STOC’12). ACM, 123--136.

Digital Library

[30]

R. Lavi and N. Nisan. 2004. Competitive analysis of incentive compatible on-line auctions. Theoretical Computer Science 310, 1--3 (2004), 159--180.

Digital Library

[31]

Shengwu Li. 2015. Obviously Strategy-Proof Mechanisms. Economic Review, forthcoming.

[32]

Y. Li. 2016. Approximation in mechanism design with interdependent values. Games and Economic Behavior 103, Supplement C (2016), 225--253.

[33]

E. Maskin and P. Dasgupta. 2000. Efficient auctions. Quarterly Journal of Economics 115 (2000), 341--388.

[34]

R. P. McAfee, J. McMillan, and P. J. Reny. 1989. Extracting the surplus in the common-value auction. Econometrica 57, 6 (1989), 1451--1459.

[35]

R. P. McAfee and P. J. Reny. 1992. Correlated information and mechanism design. Econometrica 60, 2 (1992), 395--421.

[36]

R. Motwani and P. Raghavan. 1995. Randomized Algorithms. Cambridge University Press.

Digital Library

[37]

R. B. Myerson. 1981. Optimal auction design. Mathematics of Operations Research 6, 1 (1981), 58--73.

Digital Library

[38]

C. H. Papadimitriou and G. Pierrakos. 2011. On optimal single-item auctions. In Proceedings of the 34rd Annual ACM Symposium on Theory of Computing. ACM, 119--128.

Digital Library

[39]

A. Ronen. 2001. On approximating optimal auctions. In Proceedings of the 2nd ACM Conference on Economics and Computation (EC’01). ACM, 11--17.

Digital Library

[40]

A. Ronen and A. Saberi. 2002. On the hardness of optimal auctions. In Proceedings of the 43rd Annual IEEE Symposium on Foundations of Computer Science. IEEE, 396--405.

Digital Library

[41]

T. Roughgarden and I. Talgam-Cohen. 2013. Optimal and near-optimal mechanism design with interdependent values. In Proceedings of the 13th ACM Conference on Economics and Computation (EC’13). ACM, 767--784.

Digital Library

[42]

A. Rubinstein and S. M. Weinberg. 2015. Simple mechanisms for a subadditive buyer and applications to revenue monotonicity. In Proceedings of the 16th ACM Conference on Economics and Computation (EC’15). ACM, 377--394.

Digital Library

[43]

T. Sandholm and A. Gilpin. 2004. Sequences of take-it-or-leave-it offers: Near-optimal auctions without full valuation revelation. In Agent-Mediated Electronic Commerce V. Springer.

[44]

I. Segal. 2003. Optimal pricing mechanisms with unknown demand. American Economic Review 93, 3 (2003), 509--529.

[45]

V. Syrgkanis, D. Kempe, and E. Tardos. 2015. Information asymmetries in common-value auctions with discrete signals. In Proceedings of the 16th ACM Conference on Economics and Computation. ACM, 303--303.

Digital Library

[46]

W. Vickrey. 1961. Counterspeculation, auctions, and competitive sealed tenders. Journal of Finance 16, 1 (1961), 8--37.

[47]

Q. Yan. 2011. Mechanism design via correlation gap. In Proceedings of the 22nd ACM-SIAM Symposium on Discrete Algorithms (SODA’11). SIAM, 710--719.

Digital Library

Cited By

Ferraioli DVentre CAgmon NAn BRicci AYeoh W(2023)Explicit Payments for Obviously Strategyproof MechanismsProceedings of the 2023 International Conference on Autonomous Agents and Multiagent Systems10.5555/3545946.3598886(2125-2133)Online publication date: 30-May-2023
https://dl.acm.org/doi/10.5555/3545946.3598886
Ferraioli DMeier APenna PVentre C(2023)New Constructions of Obviously Strategyproof MechanismsMathematics of Operations Research10.1287/moor.2022.126448:1(332-362)Online publication date: 1-Feb-2023
https://dl.acm.org/doi/10.1287/moor.2022.1264
Castiglioni MMarchesi ARomano GGatti N(2023)Increasing Revenue in Bayesian Posted Price Auctions through SignalingArtificial Intelligence10.1016/j.artint.2023.103990(103990)Online publication date: Aug-2023
https://doi.org/10.1016/j.artint.2023.103990

Index Terms

Sequential Posted-Price Mechanisms with Correlated Valuations
1. Applied computing
  1. Electronic commerce
    1. Online auctions
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis
    2. Online algorithms
  2. Theory and algorithms for application domains
    1. Algorithmic game theory and mechanism design
      1. Algorithmic mechanism design
      2. Computational pricing and auctions

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Published In

cover image ACM Transactions on Economics and Computation

ACM Transactions on Economics and Computation Volume 5, Issue 4

Special Issue on Wine'15

November 2017

146 pages

ISSN:2167-8375

EISSN:2167-8383

DOI:10.1145/3174276

Editors:
David Pennock
Microsoft
,
Ilya Segal
Stanford University

Issue’s Table of Contents

Copyright © 2017 ACM.

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Publication History

Published: 22 December 2017

Accepted: 01 September 2017

Revised: 01 April 2017

Received: 01 July 2016

Published in TEAC Volume 5, Issue 4

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Funding Sources

ERC StG Project PAAl
Italian MIUR PRIN 2010-2011 project ARS TechnoMedia -- Algorithmics for Social Technological Networks
Google Research Award for Economics and Market Algorithms
EU FET project MULTIPLEX
GNCS--INdAM

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Cited By

Ferraioli DVentre CAgmon NAn BRicci AYeoh W(2023)Explicit Payments for Obviously Strategyproof MechanismsProceedings of the 2023 International Conference on Autonomous Agents and Multiagent Systems10.5555/3545946.3598886(2125-2133)Online publication date: 30-May-2023
https://dl.acm.org/doi/10.5555/3545946.3598886
Ferraioli DMeier APenna PVentre C(2023)New Constructions of Obviously Strategyproof MechanismsMathematics of Operations Research10.1287/moor.2022.126448:1(332-362)Online publication date: 1-Feb-2023
https://dl.acm.org/doi/10.1287/moor.2022.1264
Castiglioni MMarchesi ARomano GGatti N(2023)Increasing Revenue in Bayesian Posted Price Auctions through SignalingArtificial Intelligence10.1016/j.artint.2023.103990(103990)Online publication date: Aug-2023
https://doi.org/10.1016/j.artint.2023.103990

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