Riccardo Colini-Baldeschi
Paul W. Goldberg
Stefano Leonardi
Abstract
We develop and extend a line of recent work on the design of mechanisms for two-sided markets. The markets we consider consist of buyers and sellers of a number of items, and the aim of a mechanism is to improve the social welfare by arranging purchases and sales of the items. A mechanism is given prior distributions on the agents’ valuations of the items, but not the actual valuations; thus, the aim is to maximise the expected social welfare over these distributions. As in previous work, we are interested in the worst-case ratio between the social welfare achieved by a truthful mechanism and the best social welfare possible.
Our main result is an incentive compatible and budget balanced constant-factor approximation mechanism in a setting where buyers have XOS valuations and sellers’ valuations are additive. This is the first such approximation mechanism for a two-sided market setting where the agents have combinatorial valuation functions. To achieve this result, we introduce a more general kind of demand query that seems to be needed in this situation. In the simpler case that sellers have unit supply (each having just one item to sell), we give a new mechanism whose welfare guarantee improves on a recent one in the literature. We also introduce a more demanding version of the strong budget balance (SBB) criterion, aimed at ruling out certain “unnatural” transactions satisfied by SBB. We show that the stronger version is satisfied by our mechanisms.
- Moshe Babaioff, Yang Cai, Yannai A. Gonczarowski, and Mingfei Zhao. 2018. The best of both worlds: Asymptotically efficient mechanisms with a guarantee on the expected gains-from-trade. In Proceedings of the 2018 ACM Conference on Economics and Computation. 373.Google Scholar
Digital Library
- Moshe Babaioff, Yang Cai, Yannai A. Gonczarowski, and Mingfei Zhao. 2018. The best of both worlds: Asymptotically efficient mechanisms with a guarantee on the expected gains-from-trade. In Proceedings of the 2018 ACM Conference on Economics and Computation. ACM, 373--373.Google ScholarDigital Library
- Moshe Babaioff, Noam Nisan, and Elan Pavlov. 2009. Mechanisms for a spatially distributed market. Games Econ. Behav. 66, 2 (2009), 660--684.Google ScholarCross Ref
- Liad Blumrosen and Shahar Dobzinski. 2014. Reallocation mechanisms. In Proceedings of the 15th ACM Conference on Economics and Computation (EC’14). ACM, 617--617.Google ScholarDigital Library
- Liad Blumrosen and Shahar Dobzinski. 2016. (Almost) efficient mechanisms for bilateral trading. ArXiv/CoRR abs/1604.04876 (2016).Google Scholar
- Liad Blumrosen and Thomas Holenstein. 2008. Posted prices vs. negotiations: An asymptotic analysis. In Proceedings of the 9th ACM conference on Electronic Commerce (EC’08). ACM, 49--49.Google ScholarDigital Library
- Liad Blumrosen and Yenohatan Mizrahi. 2016. Approximating gains-from-trade in bilateral trading. In Proceedings of the 12th International Conference on Web and Internet Economics (WINE), Yang Cai and Adrian Vetta (Eds.). Springer, 400--413.Google ScholarDigital Library
- Johannes Brustle, Yang Cai, Fa Wu, and Mingfei Zhao. 2017. Approximating gains from trade in two-sided markets via simple mechanisms. In Proceedings of the 2017 ACM Conference on Economics and Computation (EC’17). 589--590.Google ScholarDigital Library
- Shuchi Chawla, Jason D. Hartline, David L. Malec, and Balasubramanian 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.Google Scholar
- Edward H. Clarke. 1971. Multipart pricing of public goods. Publ. Choice 11, 1 (1971), 17--33.Google ScholarCross Ref
- Riccardo Colini-Baldeschi, Paul Goldberg, Bart de Keijzer, Stefano Leonardi, and Stefano Turchetta. 2017. Fixed price approximability of the optimal gain from trade. In International Conference on Web and Internet Economics. Springer, Cham.Google ScholarDigital Library
- Riccardo Colini-Baldeschi, Bart De Keijzer, Stefano Leonardi, and Stefano Turchetta. 2016. Approximately efficient double auctions with strong budget balance. In Proceedings of the 27th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’16). ACM-SIAM, 1424--1443.Google ScholarCross Ref
- Xiaotie Deng, Paul W. Goldberg, Bo Tang, and Jinshan Zhang. 2014. Revenue maximization in a Bayesian double auction market. Theor. Comput. Sci. 539, 1 (2014), 1--12.Google ScholarCross Ref
- Kaustubh Deshmukh, Andrew V. Goldberg, Jason D. Hartline, and Anna R. Karlin. 2002. Truthful and competitive double auctions. In Proceedings of the 10th Annual European Symposium on Algorithms (ESA’02). Springer, 361--373.Google Scholar
- Shahar Dobzinski, Noam Nisan, and Michael Schapira. 2010. Approximation algorithms for combinatorial auctions with complement-free bidders. Math. Operat. Res. 35, 1 (2010), 1--13.Google ScholarDigital Library
- Paul Dütting and Robert Kleinberg. 2015. Polymatroid prophet inequalities. In Proceedings of the 23rd Annual European Symposium on Algorithms (ESA’15). 437--449.Google ScholarCross Ref
- Paul Dütting, Inbal Talgam-Cohen, and Tim Roughgarden. 2014. Modularity and greed in double auctions. In Proceedings of the 15th ACM Conference on Economics and Computation (EC’14). ACM, 241--258.Google ScholarDigital Library
- Uriel Feige and Shlomo Joseph. 2014. Demand queries with preprocessing. In Proceedings of the 41st International Colloquium on Automata, Languages, and Programming (ICALP’14). LNCS 8572. Springer, Berlin, 477--488.Google ScholarCross Ref
- Michal Feldman, Nick Gravin, and Brendan Lucier. 2015. Combinatorial auctions via posted prices. In Proceedings of the 26th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’15). ACM-SIAM, 123--135.Google ScholarDigital Library
- Thomas A. Gresik and Mark A. Satterthwaite. 1989. The rate at which a simple market converges to efficiency as the number of traders increases: An asymptotic result for optimal trading mechanisms. J. Econ. Theory 48, 1 (1989), 304--332.Google ScholarCross Ref
- Theodore Groves. 1973. Incentives in teams. Econometrica 41, 4 (1973), 617--631.Google ScholarCross Ref
- Robert Kleinberg and Seth M. Weinberg. 2012. Matroid prophet inequalities. In Proceedings of the 44th Annual ACM Symposium on Theory of Computing (STOC). ACM, 123--136.Google Scholar
- Benjamin Lubin, Adam I. Juda, Ruggiero Cavallo, Sébastien Lahaie, Jeffrey Shneidman, and David C. Parkes. 2008. ICE: An expressive iterative combinatorial exchange. J. Artif. Intell. Res. 33 (2008), 33--77.Google ScholarDigital Library
- R. Preston McAfee. 1992. A dominant strategy double auction. J. Econ. Theory 56, 2 (1992), 434--450.Google ScholarCross Ref
- R. Preston McAfee. 2008. The gains from trade under fixed price mechanisms. Appl. Econ. Res. Bull. 1, 1 (2008), 1--10.Google Scholar
- Roger B. Myerson. 1981. Optimal auction design. Math. Operat. Res. 6, 1 (1981), 58--73.Google ScholarDigital Library
- Roger B. Myerson and Mark A. Satterthwaite. 1983. Efficient mechanisms for bilateral trading. J. Econ. Theory 29 (1983), 265--281.Google ScholarCross Ref
- Aldo Rustichini, Mark A. Satterthwaite, and Steven R. Williams. 1994. Convergence to efficiency in a simple market with incomplete information. Econometrica 62, 5 (1994), 1041--1063.Google ScholarCross Ref
- Tuomas Sandholm and Andrew Gilpin. 2004. Sequences of Take-It-or-Leave-It Offers: Near-Optimal Auctions Without Full Valuation Revelation. Springer, 73--91.Google Scholar
- Mark A. Satterthwaite and Steven R. Williams. 1989. The rate of convergence to efficiency in the buyer’s bid double auction as the market becomes large. Rev. Econ. Stud. 56, 4 (1989), 477--498.Google ScholarCross Ref
- Mark A. Satterthwaite and Steven R. Williams. 2002. The optimality of a simple market mechanism. Econometrica 70, 5 (2002), 1841--1863.Google ScholarCross Ref
- Erel Segal-Halevi, Avinatan Hassidim, and Yonatan Aumann. 2016. A random-sampling double-auction mechanism. CoRR abs/1604.06210 (2016).Google Scholar
- Erel Segal-Halevi, Avinatan Hassidim, and Yonatan Aumann. 2016. SBBA: A strongly-budget-balanced double-auction mechanism. In Proceedings of the 9th International Symposium on Algorithmic Game Theory (SAGT’16). Springer, 260--272.Google ScholarCross Ref
- William Vickrey. 1961. Counterspeculation, auctions, and competitive sealed tenders. J. Finan. 16, 1 (1961), 8--37.Google ScholarCross Ref
Index Terms
- Approximately Efficient Two-Sided Combinatorial Auctions
Recommendations
Approximately Efficient Two-Sided Combinatorial Auctions
EC '17: Proceedings of the 2017 ACM Conference on Economics and ComputationWe develop and extend a line of recent work on the design of mechanisms for two-sided markets. The markets we consider consist of buyers and sellers of a number of items, and the aim of a mechanism is to improve the social welfare by arranging purchases ...
Bayesian Combinatorial Auctions
We study the following simple Bayesian auction setting: m items are sold to n selfish bidders in m independent second-price auctions. Each bidder has a private valuation function that specifies his or her complex preferences over all subsets of items. ...
Revenue monotonicity in deterministic, dominant-strategy combinatorial auctions
In combinatorial auctions using VCG, a seller can sometimes increase revenue by dropping bidders. In this paper we investigate the extent to which this counterintuitive phenomenon can also occur under other deterministic, dominant-strategy combinatorial ...
Comments