research-article

Fast core pricing algorithms for path auction

Authors:

Chongjun WangAuthors Info & Claims

Autonomous Agents and Multi-Agent Systems, Volume 34, Issue 1

https://doi.org/10.1007/s10458-019-09440-y

Published: 14 January 2020 Publication History

Abstract

Path auction is held in a graph, where each edge stands for a commodity and the weight of this edge represents the prime cost. Bidders own some edges and make bids for their edges. The auctioneer needs to purchase a sequence of edges to form a path between two specific vertices. Path auction can be considered as a kind of combinatorial reverse auctions. Core-selecting mechanism is a prevalent mechanism for combinatorial auction. However, pricing in core-selecting combinatorial auction is computationally expensive, one important reason is the exponential core constraints. The same is true of path auction. To solve this computation problem, we simplify the constraint set and get the optimal set with only polynomial constraints in this paper. Based on our constraint set, we put forward two fast core pricing algorithms for the computation of bidder-Pareto-optimal core outcome. Among all the algorithms, our new algorithms have remarkable runtime performance. Finally, we validate our algorithms on real-world datasets and obtain excellent results.

References

[1]

Archer A and Tardos ÉFrugal path mechanismsACM Transactions on Algorithms (TALG)200731323018291321.68375

[2]

Ausubel LM and Milgrom PRAscending auctions with package biddingAdvances in Theoretical Economics2002111-422003257

[3]

Ausubel LM, Milgrom P, et al. The lovely but lonely Vickrey auction Combinatorial Auctions 2006 17 22-26

[4]

Bünz, B., Seuken, S., & Lubin, B. (2015). A faster core constraint generation algorithm for combinatorial auctions. In Twenty-Ninth AAAI conference on artificial intelligence (pp. 827–834).

[5]

Bünz, B., Lubin, B., & Seuken, S. (2018). Designing core-selecting payment rules: A computational search approach. In Proceedings of the 2018 ACM conference on economics and computation (pp. 109–109). ACM.

[6]

Cheng, H., Zhang, L., Zhang, Y., Wu, J., & Wang, C. (2018). Optimal constraint collection for core-selecting path mechanism. In Proceedings of the 17th international conference on autonomous agents and multiagent systems (pp. 41–49).

[7]

Clarke EH Multipart pricing of public goods Public Choice 1971 11 1 17-33

[8]

Cramton P Spectrum auction design Review of Industrial Organization 2013 42 2 161-190

[9]

Day, R., & Milgrom, P. (2013). Optimal incentives in core-selecting auctions. In The handbook of market design (Chap. 11, pp. 282–298). OUP Oxford.

[10]

Day R and Milgrom PCore-selecting package auctionsInternational Journal of Game Theory2008363–4393-40723834681151.91073

[11]

Day RW and Cramton PQuadratic core-selecting payment rules for combinatorial auctionsOperations Research2012603588-60329605311251.90302

[12]

Day RW and Raghavan SFair payments for efficient allocations in public sector combinatorial auctionsManagement Science20075391389-14061232.91286

[13]

Du Y, Sami R, and Shi YPath auctions with multiple edge ownershipTheoretical Computer Science20104111293-30025883761187.91029

[14]

Elkind, E., Sahai, A., & Steiglitz, K. (2004). Frugality in path auctions. In Proceedings of the fifteenth annual ACM-SIAM symposium on discrete algorithms (pp. 701–709). Society for Industrial and Applied Mathematics

[15]

Erdil A and Klemperer P A new payment rule for core-selecting package auctions Journal of the European Economic Association 2010 8 2–3 537-547

[16]

Feigenbaum J, Papadimitriou C, Sami R, and Shenker SA BGP-based mechanism for lowest-cost routingDistributed Computing200518161-721264.68215

[17]

Grötschel M, Lovász L, and Schrijver AThe ellipsoid method and its consequences in combinatorial optimizationCombinatorica198112169-1976255500492.90056

[18]

Groves T et al.Incentives in teamsEconometrica1973414617-6314412640311.90002

[19]

Hartline, J., Immorlica, N., Khani, M.R., Lucier, B., & Niazadeh, R. (2018). Fast core pricing for rich advertising auctions. In Proceedings of the 2018 ACM conference on economics and computation (pp. 111–112). ACM.

[20]

Hershberger, J., & Suri, S. (2001). Vickrey prices and shortest paths: What is an edge worth? In Proceedings 42nd IEEE symposium on foundations of computer science (pp. 252–259). IEEE.

[21]

Karger, D., & Nikolova, E. (2006). On the expected VCG overpayment in large networks. In Proceedings of the 45th IEEE conference on decision and control (pp. 2831–2836).

[22]

Karlin, A.R., Kempe, D., & Tamir, T. (2005). Beyond VCG: Frugality of truthful mechanisms. In 46th annual IEEE symposium on foundations of computer science (FOCS’05) (pp. 615–626). IEEE.

[23]

Lee, Y. T., Sidford, A., & Wong, S. C. W. (2015). A faster cutting plane method and its implications for combinatorial and convex optimization. In 56th annual symposium on foundations of computer science (pp. 1049–1065). IEEE.

[24]

Lehmann D, Oćallaghan LI, and Shoham YTruth revelation in approximately efficient combinatorial auctionsJournal of the ACM (JACM)2002495577-60221470931326.91011

[25]

Leskovec, J., & Krevl, A. (2014, June). SNAP datasets: Stanford large network dataset collection. http://snap.stanford.edu/data/.

[26]

Nisan, N., & Ronen, A. (1999). Algorithmic mechanism design. In Proceedings of the thirty-first annual ACM symposium on theory of computing (pp. 129–140). ACM.

[27]

Polymenakos L and Bertsekas DPParallel shortest path auction algorithmsParallel Computing19942091221-124712932530823.68086

[28]

Rothkopf MH, Pekeč A, and Harstad RMComputationally manageable combinational auctionsManagement science19984481131-11470989.90094

[29]

Vickrey WCounterspeculation, auctions, and competitive sealed tendersThe Journal of Finance19611618-373363406

[30]

Yokoo M, Sakurai Y, and Matsubara SThe effect of false-name bids in combinatorial auctions: New fraud in internet auctionsGames and Economic Behavior2004461174-18820275071069.91039

[31]

Zhang, L., Chen, H., Wu, J., Wang, C. J., & Xie, J. (2016). False-name-proof mechanisms for path auctions in social networks. In ECAI (pp. 1485–1492).

[32]

Zhu Y, Li B, Fu H, and Li Z Core-selecting secondary spectrum auctions IEEE Journal on Selected Areas in Communications 2014 32 11 2268-2279

Cited By

Fritsch RLee YMeier AWang YWattenhofer R(2023)Understanding the Relationship Between Core Constraints and Core-Selecting Payment Rules in Combinatorial AuctionsFrontiers of Algorithmics10.1007/978-3-031-39344-0_1(1-14)Online publication date: 14-Aug-2023
https://dl.acm.org/doi/10.1007/978-3-031-39344-0_1

Index Terms

Fast core pricing algorithms for path auction

Index terms have been assigned to the content through auto-classification.

Recommendations

Pricing Rule in a Clock Auction

We analyze a discrete clock auction with lowest-accepted-bid (LAB) pricing and provisional winners, as adopted by India for its 3G spectrum auction. In a perfect Bayesian equilibrium, the provisional winner shades her bid, whereas provisional losers do ...
Core-selecting package auctions
Abstract
Auctions that select core allocations with respect to reported values generate competitive levels of sales revenues at equilibrium and limit bidder incentives to use shills. Among core-selecting auctions, the ones that minimize seller revenues ...
Optimal Constraint Collection for Core-Selecting Path Mechanism
AAMAS '18: Proceedings of the 17th International Conference on Autonomous Agents and MultiAgent Systems

In path auctions, strategic bidders make bids for commodities. Each edge of the graph stands for a commodity and the weight on the edge represents the prime cost. Auctioneer needs to purchase a sequence of edges in order to get a path from one vertex to ...

Comments

Information & Contributors

Information

Published In

cover image Autonomous Agents and Multi-Agent Systems

Autonomous Agents and Multi-Agent Systems Volume 34, Issue 1

Mar 2020

1000 pages

ISSN:1387-2532

Issue’s Table of Contents

© Springer Science+Business Media, LLC, part of Springer Nature 2020.

Publisher

Kluwer Academic Publishers

United States

Publication History

Published: 14 January 2020

Author Tags

Qualifiers

Research-article

Funding Sources

National Key Research and Development Program of China
National Natural Science Foundation of China

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

1
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 21 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Fritsch RLee YMeier AWang YWattenhofer R(2023)Understanding the Relationship Between Core Constraints and Core-Selecting Payment Rules in Combinatorial AuctionsFrontiers of Algorithmics10.1007/978-3-031-39344-0_1(1-14)Online publication date: 14-Aug-2023
https://dl.acm.org/doi/10.1007/978-3-031-39344-0_1

View Options

View options

Media

Figures

Other

Tables

View Issue’s Table of Contents