Document Open Access Logo

Walrasian Pricing in Multi-Unit Auctions

Authors Simina Brânzei, Aris Filos-Ratsikas, Peter Bro Miltersen, Yulong Zeng



PDF
Thumbnail PDF

File

LIPIcs.MFCS.2017.80.pdf
  • Filesize: 0.51 MB
  • 14 pages

Document Identifiers

Author Details

Simina Brânzei
Aris Filos-Ratsikas
Peter Bro Miltersen
Yulong Zeng

Cite AsGet BibTex

Simina Brânzei, Aris Filos-Ratsikas, Peter Bro Miltersen, and Yulong Zeng. Walrasian Pricing in Multi-Unit Auctions. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 80:1-80:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.MFCS.2017.80

Abstract

Multi-unit auctions are a paradigmatic model, where a seller brings multiple units of a good, while several buyers bring monetary endowments. It is well known that Walrasian equilibria do not always exist in this model, however compelling relaxations such as Walrasian envy-free pricing do. In this paper we design an optimal envy-free mechanism for multi-unit auctions with budgets. When the market is even mildly competitive, the approximation ratios of this mechanism are small constants for both the revenue and welfare objectives, and in fact for welfare the approximation converges to 1 as the market becomes fully competitive. We also give an impossibility theorem, showing that truthfulness requires discarding resources, and in particular, is incompatible with (Pareto) efficiency.
Keywords
  • mechanism design
  • multi-unit auctions
  • Walrasian pricing
  • market share

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. E. Anderson and D. Simester. Price stickiness and customer antagonism. Available at SSRN 1273647, 2008. Google Scholar
  2. L. M. Ausubel. An efficient ascending-bid auction for multiple objects. The American Economic Review, 94(5):1452-1475, 2004. Google Scholar
  3. M. Babaioff, B. Lucier, N. Nisan, and R. Paes Leme. On the efficiency of the walrasian mechanism. In ACM EC, pages 783-800. ACM, 2014. Google Scholar
  4. M. F. Balcan, A. Blum, and Y. Mansour. Item pricing for revenue maximization. In ACM EC, pages 50-59. ACM, 2008. Google Scholar
  5. Y. Bartal, R. Gonen, and N. Nisan. Incentive compatible multi unit combinatorial auctions. In TARK, pages 72-87, 2003. Google Scholar
  6. C. Borgs, J. Chayes, N. Immorlica, M. Mahdian, and A. Saberi. Multi-unit auctions with budget-constrained bidders. In ACM EC, pages 44-51, 2005. Google Scholar
  7. A. Borodin, O. Lev, and T. Strangway. Budgetary effects on pricing equilibrium in online markets. In AAMAS, 2016. Google Scholar
  8. S. Brânzei, Y. Chen, X. Deng, A. Filos-Ratsikas, S. K. S. Frederiksen, and J. Zhang. The fisher market game: Equilibrium and welfare. In AAAI, pages 587-593, 2014. Google Scholar
  9. Simina Brânzei and Ariel D. Procaccia. Verifiably truthful mechanisms. In ITCS, pages 297-306, 2015. Google Scholar
  10. Y. Cai, C. Daskalakis, and M. Weinberg. Optimal multi-dimensional mechanism design: Reducing revenue to welfare maximization. In FOCS, pages 130-139, 2012. Google Scholar
  11. Y. Cai, C. Daskalakis, and M. Weinberg. Reducing revenue to welfare maximization: Approximation algorithms and other generalizations. In SODA, pages 578-595, 2013. Google Scholar
  12. N. Chen, X. Deng, and J. Zhang. How profitable are strategic behaviors in a market? In ESA, pages 106-118. Springer, 2011. Google Scholar
  13. M. Cheung and C. Swamy. Approximation algorithms for single-minded envy-free profit-maximization problems with limited supply. In FOCS, pages 35-44, 2008. Google Scholar
  14. V. Cohen-Addad, A. Eden, M. Feldman, and A. Fiat. The invisible hand of dynamic market pricing. In ACM EC, pages 383-400, 2016. Google Scholar
  15. R. Colini-Baldeschi, S. Leonardi, P. Sankowski, and Q. Zhang. Revenue maximizing envy-free fixed-price auctions with budgets. In WINE, pages 233-246. Springer, 2014. Google Scholar
  16. S. Dobzinski, R. Lavi, and N. Nisan. Multi-unit auctions with budget limits. GEB, 74(2):486-503, 2012. Google Scholar
  17. S. Dobzinski and R. P. Leme. Efficiency guarantees in auctions with budgets. In ICALP, pages 392-404. Springer, 2014. Google Scholar
  18. S. Dobzinski and N. Nisan. Mechanisms for multi-unit auctions. In ACM EC, pages 346-351, 2007. Google Scholar
  19. S. Dobzinski and N. Nisan. Multi-unit auctions: beyond roberts. JET, 156:14-44, 2015. Google Scholar
  20. A. Eden, M. Feldman, O. Friedler, I. Talgam-Cohen, and M. Weinberg. The competition complexity of auctions: A bulow-klemperer result for multi-dimensional bidders. In ACM EC, 2017. Google Scholar
  21. P. Farris, N. Bendle, P. Pfeifer, and D. Reibstein. Marketing metrics: The definitive guide to measuring marketing performance. Pearson Education, 2010. Google Scholar
  22. M. Feldman, A. Fiat, S. Leonardi, and P. Sankowski. Revenue maximizing envy-free multi-unit auctions with budgets. In ACM EC, pages 532-549, 2012. Google Scholar
  23. M. Feldman, N. Gravin, and B. Lucier. Combinatorial auctions via posted prices. In SODA, pages 123-135, 2015. Google Scholar
  24. F. Gul and E. Stacchetti. Walrasian equilibrium with gross substitutes. Journal of Economic Theory, 87(1):95-124, 1999. Google Scholar
  25. V. Guruswami, J. Hartline, A. Karlin, D. Kempe, C. Kenyon, and F. McSherry. On profit-maximizing envy-free pricing. In SODA, pages 1164-1173, 2005. Google Scholar
  26. Sergiu Hart and Noam Nisan. The menu-size complexity of auctions. In ACM EC, pages 565-566, 2013. Google Scholar
  27. J. Hartline and T. Roughgarden. Simple versus optimal mechanisms. In ACM EC, pages 225-234. ACM, 2009. Google Scholar
  28. J. Hartline and Q. Yan. Envy, truth, and profit. In ACM EC, pages 243-252, 2011. Google Scholar
  29. J. D. Hartline. Mechanism design and approximation. Book draft. October, 122, 2013. Google Scholar
  30. A. S. Kelso and V. P. Crawford. Job matching, coalition formation, and gross substitutes. Econometrica, 50:1483-1504, 1982. Google Scholar
  31. Shengwu Li. Obviously strategy-proof mechanisms, 2015. Working paper. Google Scholar
  32. E. Markakis and O. Telelis. Envy-free revenue approximation for asymmetric buyers with budgets. In SAGT, pages 247-259, 2016. Google Scholar
  33. R. Mehta and M. Sohoni. Exchange markets: Strategy meets supply-awareness. In WINE, pages 361-362. Springer, 2013. Google Scholar
  34. R. Mehta, N. Thain, L. Végh, and A. Vetta. To save or not to save: The fisher game. In WINE, pages 294-307. Springer, 2014. Google Scholar
  35. R. B. Myerson. Optimal auction design. MOR, 6(1):58-73, 1981. Google Scholar
  36. N. Nisan, T. Roughgarden, E. Tardos, and V. Vazirani. Algorithmic Game Theory. Cambridge Univ. Press, (editors) 2007. Google Scholar
  37. M. Petersen. Information: Hard and soft, 7 2004. Google Scholar
  38. Shreyas Sekar. Posted pricing sans discrimination. In IJCAI, to appear, 2017. Google Scholar
  39. L. Walras. Elements d'economie politique pure, ou theorie de la richesse sociale (in french), 1874. English translation: Elements of pure economics; or, the theory of social wealth. American Economic Association and the Royal Economic Society, 1954. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail