Advertisement

On Revenue-Maximizing Walrasian Equilibria for Size-Interchangeable Bidders

  • Enrique Areyan ViqueiraEmail author
  • Amy Greenwald
  • Victor Naroditskiy
  • Daniels Collins
Conference paper
Part of the Lecture Notes in Business Information Processing book series

Abstract

We study a market setting in which bidders are single-valued but size-interchangeable, and there exist multiple copies of heterogeneous goods. Our contributions are as follows: (1) providing polynomial-time algorithms for finding a restricted envy-free equilibrium with reserve prices (EFEr); (2) posing the problem of finding a revenue-maximizing EFEr, and running experiments to show that our algorithms perform well on the metrics of revenue, efficiency, and time, without incurring too many violations of the stronger Walrasian equilibrium with reserve (envy-free plus market clearance) conditions.

Keywords

Reserve Price Market Maker Valuation Function Walrasian Equilibrium Feasible Allocation 
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.

References

  1. 1.
    Briest, P.: Uniform budgets and the envy-free pricing problem. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008. LNCS, vol. 5125, pp. 808–819. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-70575-8_66 CrossRefGoogle Scholar
  2. 2.
    Chen, N., Deng, X.: Envy-free pricing in multi-item markets. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6199, pp. 418–429. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-14162-1_35 CrossRefGoogle Scholar
  3. 3.
    Chen, N., Deng, X., Goldberg, P.W., Zhang, J.: On revenue maximization with sharp multi-unit demands. J. Comb. Optim. 31(3), 1174–1205 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Cheung, M., Swamy, C.: Approximation algorithms for single-minded envy-free profit-maximization problems with limited supply. In: IEEE 49th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2008, pp. 35–44. IEEE (2008)Google Scholar
  5. 5.
    Crawford, V.P., Knoer, E.M.: Job matching with heterogeneous firms and workers. Econometrica J. Econometric Soc. 49(2), 437–450 (1981)CrossRefzbMATHGoogle Scholar
  6. 6.
    Gul, F., Stacchetti, E.: Walrasian equilibrium with gross substitutes. J. Econ. Theory 87(1), 95–124 (1999). http://EconPapers.repec.org/RePEc:eee:jetheo:v:87:y:1999:i:1:p:95-124 MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Guruswami, V., Hartline, J.D., Karlin, A.R., Kempe, D., Kenyon, C., McSherry, F.: On profit-maximizing envy-free pricing. In: Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1164–1173. Society for Industrial and Applied Mathematics (2005)Google Scholar
  8. 8.
    Huang, L.S., Li, M., Zhang, B.: Approximation of Walrasian equilibrium in single-minded auctions. Theor. comput. sci. 337(1), 390–398 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Monaco, G., Sankowski, P., Zhang, Q.: Revenue maximization envy-free pricing for homogeneous resources. In: Proceedings of the 24th International Conference on Artificial Intelligence, pp. 90–96. AAAI Press (2015)Google Scholar
  10. 10.
    Myerson, R.B.: Optimal auction design. Math. Oper. Res. 6(1), 58–73 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V.V.: Algorithmic Game Theory. Cambridge University Press, New York (2007)CrossRefzbMATHGoogle Scholar
  12. 12.
    Tan, K.T.K.: The first fundamental theorem of welfare economics (2008) (Unpublished)Google Scholar
  13. 13.
    Vickrey, W.: Counterspeculation, auctions, and competitive sealed tenders. J. Finan. 16(1), 8–37 (1961)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Walras, L.: Elements of Pure Economics: Or the Theory of Social Wealth. Elements of Pure Economics, Or the Theory of Social Wealth, Routledge (2003). https://books.google.com/books?id=hwjRD3z0Qy4C
  15. 15.
    Wellman, M., Wurman, P.R.: A trading agent competition for the research community. In: IJCAI-99 Workshop on Agent-Mediated Electronic Trading (1999)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Enrique Areyan Viqueira
    • 1
    Email author
  • Amy Greenwald
    • 1
  • Victor Naroditskiy
    • 1
  • Daniels Collins
    • 1
  1. 1.Brown UniversityProvidenceUSA

Personalised recommendations