Papers
Topics
Authors
Recent
Search
2000 character limit reached

A Simplified Analysis of the Ascending Auction to Sell a Matroid Base

Published 18 Apr 2024 in cs.GT | (2404.12121v2)

Abstract: We give a simpler analysis of the ascending auction of Bikhchandani, de Vries, Schummer, and Vohra to sell a welfare-maximizing base of a matroid at Vickrey prices. The new proofs for economic efficiency and the charge of Vickrey prices only require a few matroid folklore theorems, therefore shortening the analysis of the design goals of the auction significantly.

Authors (2)
Definition Search Book Streamline Icon: https://streamlinehq.com
References (38)
  1. Ascending auctions with package bidding. The BE Journal of Theoretical Economics, 1(1):20011001, 2002.
  2. Lawrence M. Ausubel. An efficient ascending-bid auction for multiple objects. American Economic Review, 94(5):1452–1475, 2004.
  3. Lawrence M. Ausubel. An efficient dynamic auction for heterogeneous commodities. American Economic Review, 96(3):602–629, 2006.
  4. Ascending auctions for integral (poly)matroids with concave nondecreasing separable values. In Shang-Hua Teng, editor, Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2008, San Francisco, California, USA, January 20-22, 2008, pages 864–873. SIAM, 2008.
  5. An ascending vickrey auction for selling bases of a matroid. Operations research, 59(2):400–413, 2011.
  6. On the computational power of iterative auctions. In Proceedings of the 6th ACM Conference on Electronic Commerce, pages 29–43, 2005.
  7. Mechanisms for a spatially distributed market. In Proceedings of the 5th ACM Conference on Electronic Commerce, pages 9–20, 2004.
  8. Richard A. Brualdi. Comments on bases in dependence structures. Bulletin of the Australian Mathematical Society, 1(2):161–167, 1969.
  9. Edward H. Clarke. Multipart pricing of public goods. Public choice, 11(1):17–33, 1971.
  10. Peter Cramton. Ascending auctions. European Economic Review, 42(3-5):745–756, 1998.
  11. Jeremy E. Dawson. Optimal matroid bases: An algorithm based on cocircuits. The Quarterly Journal of Mathematics, 31(1):65–69, 1980.
  12. Multi-item auctions. Journal of political economy, 94(4):863–872, 1986.
  13. On ascending vickrey auctions for heterogeneous objects. Journal of Economic Theory, 132(1):95–118, 2007.
  14. Faster ascending auctions via polymatroid sum. arXiv preprint arXiv:2310.08454, 2023.
  15. A note on Kelso and Crawford’s gross substitutes condition. Mathematics of Operations Research, 28(3):463–469, 2003.
  16. Theodore Groves. Incentives in teams. Econometrica: Journal of the Econometric Society, pages 617–631, 1973.
  17. Walrasian equilibrium with gross substitutes. Journal of Economic theory, 87(1):95–124, 1999.
  18. The english auction with differentiated commodities. Journal of Economic theory, 92(1):66–95, 2000.
  19. Thorkell Helgason. Aspects of the theory of hypermatroids. In Hypergraph Seminar: Ohio State University 1972, pages 191–213. Springer, 1972.
  20. Alexander S. Kelso Jr. and Vincent P. Crawford. Job matching, coalition formation, and gross substitutes. Econometrica: Journal of the Econometric Society, pages 1483–1504, 1982.
  21. Renato Paes Leme. Gross substitutability: An algorithmic survey. Games and Economic Behavior, 106:294–316, 2017.
  22. Ascending price vickrey auctions for general valuations. Journal of Economic Theory, 132(1):335–366, 2007.
  23. Computing a walrasian equilibrium in iterative auctions with multiple differentiated items. In International Symposium on Algorithms and Computation, pages 468–478. Springer, 2013.
  24. Time bounds for iterative auctions: A unified approach by discrete convex analysis. Discrete Optimization, 19:36–62, 2016.
  25. Roger B. Myerson. Optimal auction design. Mathematics of operations research, 6(1):58–73, 1981.
  26. Algorithmic Game Theory. Cambridge University Press, 2007.
  27. James G. Oxley. Matroid theory, volume 3. Oxford University Press, USA, 2006.
  28. David C. Parkes. Iterative combinatorial auctions. MIT press, 2006.
  29. Iterative combinatorial auctions: Theory and practice. Aaai/iaai, 7481:53, 2000.
  30. Preventing strategic manipulation in iterative auctions: Proxy agents and price-adjustment. Aaai/iaai, 2000.
  31. Stephen Raach. Implementing efficient outcomes in combinatorial allocation problems. PhD thesis, Universität Trier, 2023.
  32. Pairwise kidney exchange. Journal of Economic theory, 125(2):151–188, 2005.
  33. Alexander Schrijver. Combinatorial optimization: polyhedra and efficiency, volume 24. Springer, 2003.
  34. Multiclass queueing systems: Polymatroidal structure and optimal scheduling control. Operations Research, 40(3-supplement-2):S293–S299, 1992.
  35. David N. C. Tse and Stephen V. Hanly. Multiaccess fading channels. i. polymatroid structure, optimal resource allocation and throughput capacities. IEEE Transactions on Information theory, 44(7):2796–2815, 1998.
  36. William Vickrey. Counterspeculation, auctions, and competitive sealed tenders. The Journal of finance, 16(1):8–37, 1961.
  37. Léon Walras. Éléments d’économie politique pure ou théorie de la richesse sociale. F. Rouge, 1874.
  38. Hassler Whitney. On the abstract properties of linear dependence. American Journal of Mathematics, 57:509–533, 1935.

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Collections

Sign up for free to add this paper to one or more collections.

Sign Up

Tweets

Sign up for free to view the 1 tweet with 0 likes about this paper.

Sign Up for Free