Computation and Incentives of Competitive Equilibria in a Matching Market

  • Ning Chen
  • Xiaotie Deng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6982)


Matching market and its many variants have been an intensively studied problem in Economics and Computer Science. In many applications centralized prices are used to determine allocations of indivisible items under the principles of individual optimization and market clearance, based on public knowledge of individual preferences. Alternatively, auction mechanisms have been used with a different set of principles for the determination of prices, based on individuals’ incentives to report their preferences.

This talk considers matching markets run by a single seller with an objective of maximizing revenue of the seller, who employs a market equilibrium pricing for allocation. We will give a polynomial time algorithm to compute such an equilibrium given budget constraints, and show that the maximum revenue market equilibrium mechanism converges, under an optimal dynamic re-bidding sequence of the buyers, to a solution equivalent to the minimum revenue equilibrium under the true preferences of buyers, which in turn is revenue equivalent to a VCG solution.

We will also discuss other related issues as well as open problems.


Market Equilibrium Competitive Equilibrium Market Maker Combinatorial Auction Price Auction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aggarwal, G., Muthukrishnan, S., Pal, D., Pal, M.: General Auction Mechanism for Search Advertising. In: WWW 2009, pp. 241–250 (2009)Google Scholar
  2. 2.
    Ashlagi, I., Braverman, M., Hassidim, A., Lavi, R., Tennenholtz, M.: Position Auctions with Budgets: Existence and Uniqueness. The B.E. Journal of Theoretical Economics 10(1), 20 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Ausubel, L., Milgrom, P.: The Lovely but Lonely Vickrey Auction. In: Cramton, P., Steinberg, R., Shoham, Y. (eds.) Combinatorial AuctionsGoogle Scholar
  4. 4.
    Bu, T., Deng, X., Qi, Q.: Forward Looking Nash Equilibrium in Keyword Auction. IPL 105(2), 41–46 (2008)CrossRefzbMATHGoogle Scholar
  5. 5.
    Bu, T., Deng, X., Qi, Q.: Arbitrage opportunities across sponsored search markets. Theor. Comput. Sci. 407(1-3), 182–191 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Bu, T., Liang, L., Qi, Q.: On Robustness of Forward-looking in Sponsored Search Auction. Algorithmica 58(4), 970–989 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Cary, M., Das, A., Edelman, B., Giotis, I., Heimerl, K., Karlin, A., Mathieu, C., Schwarz, M.: On Best-Response Bidding in GSP Auctions. In: EC 2007, pp. 262–271 (2007)Google Scholar
  8. 8.
    Chen, N., Deng, X.: On Nash Dynamics of Matching Market Equilibria, CoRR abs/1103.4196 (2011)Google Scholar
  9. 9.
    Chen, N., Deng, X., Ghosh, A.: Competitive equilibria in matching markets with budgets. SIGecom Exchanges 9(1) (2010)Google Scholar
  10. 10.
    Chen, N., Deng, X., Zhang, J.: How Profitable are Strategic Behaviors in a Market? In: Demetrescu, C., Halldórsson, M.M. (eds.) ESA 2011. LNCS, vol. 6942, pp. 106–118. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  11. 11.
    Cramton, P.: The FCC Spectrum Auctions: An Early Assessment. Journal of Economics and Management Strategy 6(3), 431–495 (1997)CrossRefGoogle Scholar
  12. 12.
    Edelman, B., Ostrovsky, M., Schwarz, M.: Internet Advertising and the Generalized Second-Price Auction. American Economic Review 97(1), 242–259 (2007)CrossRefGoogle Scholar
  13. 13.
    Langford, J., Li, L., Vorobeychik, Y., Wortman, J.: Maintaining Equilibria During Exploration in Sponsored Search Auctions. Algorithmica 58, 990–1021 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Leme, R., Tardos, E.: Pure and Bayes-Nash Price of Anarchy for Generalized Second Price Auction. In: FOCS 2010 (2010)Google Scholar
  15. 15.
    Myerson, R.: Optimal Auction Design. Mathematics of Operations Research 6, 58–73 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Nisan, N., Schapira, M., Valiant, G., Zoha, A.: Best Response Auctions. In: EC 2011 (2011)Google Scholar
  17. 17.
    Pai, M.: Competition in Mechanism. ACM Sigecom Exchange 9(1) (2010)Google Scholar
  18. 18.
    Smith, A.: An Inquiry into the Nature and Causes of the Wealth of Nations. University of Chicago Press, Chicago (1977)CrossRefGoogle Scholar
  19. 19.
    Varian, H.: Position Auctions. International Journal of Industrial Organization 6, 1163–1178 (2007)CrossRefGoogle Scholar
  20. 20.
    Vickrey, W.: Counterspeculation, Auctions, and Competitive Sealed Tenders. Journal of Finance 16, 8–37 (1961)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Walras, L.: Éléments d’économie politique pure, ou théorie de la richesse sociale (Elements of Pure Economics, or the theory of social wealth) (1874)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Ning Chen
    • 1
  • Xiaotie Deng
    • 2
  1. 1.Division of Mathematical Sciences, School of Physical and Mathematical SciencesNanyang Technological UniversitySingapore
  2. 2.Department of Computer ScienceUniversity of LiverpoolUK

Personalised recommendations