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Encyclopedia of Algorithms pp 997–1001Cite as

Utilitarian Mechanism Design for Single-Minded Agents

2005; Briest, Krysta, Vöcking

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Keywords and Synonyms

Forward (combinatorial, multi-unit) auction                    

Problem Definition

This problem deals with the design of efficiently computable incentive compatible, or truthful, mechanisms for combinatorial optimization problems with selfish one-parameter agents and a single seller. The focus is on approximation algorithms for NP-hard mechanism design problems. These algorithms need to satisfy certain monotonicity properties to ensure truthfulness.

A one parameter agent is an agent who as her private data has some resource as well as a valuation, i. e., the maximum amount of money she is willing to pay for this resource. Sometimes, however, the resource is assumed to be known to the mechanism. The scenario where a single seller offers these resources to the agents is primarily considered. Typically, the seller aims at maximizing the social welfare or her revenue. The work by Briest, Krysta and Vöcking [6] will mostly be considered, but also other existing models and results will be...

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Notes

  1. 1.

    In the case of unknown single-minded bidders, the bidders have as private data not only their valuations (as in the case of known single-minded bidders) but also the sets they demand.

Recommended Reading

  1. Andelman, N., Mansour, Y.: A sufficient condition for truthfulness with single parameter agents. In: Proc. 8th ACM Conference on Electronic Commerce (EC),Ann, Arbor, Michigan, June (2006)

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  2. Archer, A., Papadimitriou, C.H., Talwar, K., Tardos, E.: An approximate truthful mechanism for combinatorial auctions with single parameter agents. In: Proc. 14th Ann. ACM–SIAM Symp. on Discrete Algorithms (SODA), pp. 205–214. Baltimore, Maryland (2003)

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  3. Awerbuch, B., Azar, Y., Meyerson, A.: Reducing truth-telling online mechanisms to online optimization. In: Proc. 35th Ann. ACM. Symp. on Theory of Comput. (STOC), San Diego, California (2003)

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  4. Azar, Y., Gamzu, I., Gutner, S.: Truthful unsplittable flow for large capacity networks. In: Proc. 19th Ann. ACM Symp. on Parallelism in Algorithms and Architectures (SPAA), pp. 320–329 (2007)

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  5. Bartal, Y., Gonen, R., Nisan, N.: Incentive compatible multi unit combinatorial auctions. In: Proceedings of the 9th conference on Theoretical aspects of rationality and knowledge (TARK), pp. 72–87. ACM Press (2003). http://doi.acm.org/10.1145/846241.846250

  6. Briest, P., Krysta, P., Vöcking, B.: Approximation techniques for utilitarian mechanism design. In: Proc. 37th Ann. ACM. Symp. on Theory of Comput. (STOC), pp. 39–48 (2005)

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  7. Fiat, A., Goldberg, A.V., Hartline, J.D., Karlin, A.R.: Competitive generalized auctions. In: Proc. 34th Ann. ACM. Symp. on Theory of Comput. (STOC), pp. 72–81 (2002)

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  8. Goldberg, A.V., Hartline, J.D., Wright, A.: Competitive auctions and digital goods. In: Proc. 12th Ann. ACM–SIAM Symp. on Discrete Algorithms (SODA), pp. 735–744 (2001)

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  9. Krysta, P.: Greedy approximation via duality for packing, combinatorial auctions and routing. In: Proc. 30th Int. Conference on Mathematical Foundations of Comput. Sci. (MFCS). Lecture Notes in Computer Science, vol. 3618, pp. 615–627 (2005)

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  11. Mu'alem, A., Nisan, N.: Truthful approximation mechanisms for restricted combinatorial auctions. In: Proc. 18th Nat. Conf. Artificial Intelligence, pp. 379–384. AAAI (2002)

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  12. Myerson, R.B.: Optimal auction design. Math. Oper. Res. 6, 58–73 (1981)

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  13. Ronen, A.: On approximating optimal auctions (extended abstract). In: Proc. 3rd ACM Conference on Electronic Commerce (EC), pp. 11–17 (2001)

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  14. Ronen, A., Saberi, A.: On the hardness of optimal auctions. In: Proc. 43rd Ann. IEEE Symp. on Foundations of Comput. Sci. (FOCS), pp. 396–405 (2002)

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Liverpool, Liverpool, UK

    Piotr Krysta

  2. Department of Computer Science, RWTH Aachen University, Aachen, Germany

    Berthold Vöcking

Authors
  1. Piotr Krysta
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  2. Berthold Vöcking
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer ScienceMcCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL, 60208, USA

    Ming-Yang Kao Professor of Computer Science

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© 2008 Springer-Verlag

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Krysta, P., Vöcking, B. (2008). Utilitarian Mechanism Design for Single-Minded Agents. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_454

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