An optimal auction for capacity constrained bidders: a network perspective

Abstract

This paper examines the problem of a seller with limited supply selling to a group of agents whose private information is two-dimensional. Each agent has a constant marginal value for the good up to some capacity, thereafter it is zero. Both the marginal value and the capacity are private information. We describe the revenue maximizing Bayesian incentive compatible auction for this environment. A novel feature of the analysis is an interpretation of an optimal auction design problem in terms of a linear program that is an instance of a parametric shortest path problem on a lattice.

This is a preview of subscription content, access via your institution.

References

  1. Ahuja R., Magananti T. and Orlin J. (1993). Network flows. New Jersey, Prentice Hall

    Google Scholar 

  2. Armstrong M. (1996). Multiproduct nonlinear pricing. Econometrica 64: 51–75

    Article  Google Scholar 

  3. Armstrong M. (2000). Optimal multi-object auctions. Rev Econ Stud 67: 455–481

    Article  Google Scholar 

  4. Armstrong M. and Rochet J.-C. (1999). Multi-dimensional screening: a user’s guide. Eur Econ Rev 43: 959–979

    Article  Google Scholar 

  5. Ausubel L.M. (2004). An efficient ascending-bid auction for multiple objects. Am Econ Rev 94: 1452–1475

    Article  Google Scholar 

  6. Avery C. and Hendershott T. (2000). Bundling and optimal auctions on multiple products. Rev Econ Stud 67: 483–497

    Article  Google Scholar 

  7. Dana J. (1993). The organization and scope of agents: regulating multiproduct industries. J Econ Theory 59: 228–310

    Google Scholar 

  8. Malakhov, A., Vohra, R.V.: Single and multi-dimensional auctions—a network approach. CMS-EMS Discussion Paper 1397, Northwestern University (2004)

  9. Manelli, A., Vincent, D.: Multidimensional mechanism design: revenue maximization and the multiple-good monopoly. FEEM Working Paper 153.04 (2004)

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

    Article  Google Scholar 

  11. Rochet J.-C. (1987). A necessary and sufficient condition for rationalizability in a quasi-linear context. J Math Econ 16: 191–200

    Article  Google Scholar 

  12. Rochet J.-C. and Stole L.A. (2003). The economics of multidimensional screening. In: Dewatripont, M., Hansen, L.P. and Turnovsky, S.J. (eds) Advances in Economics and Econometrics: Theory and Applications, 8th world congress, pp. Cambridge University Press, Cambridge

    Google Scholar 

  13. Ronen, A., Saberi, A.: Optimal auctions are hard. In: Proceedings of the 43rd annual IEEE symposium on foundations of computer science. Vancouver (2002)

  14. Wilson R. (1993). Non linear pricing. Oxford University Press, Oxford

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Alexey Malakhov.

Additional information

We thank the referees for a number of useful suggestions that have been incorporated into the paper. Mallesh Pai suggested the argument given in Lemma 1. The research was supported in part by the NSF grant ITR IIS-0121678.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Malakhov, A., Vohra, R.V. An optimal auction for capacity constrained bidders: a network perspective. Econ Theory 39, 113–128 (2009). https://doi.org/10.1007/s00199-007-0312-x

Download citation

Keywords

  • Auctions
  • Networks
  • Linear programming

JEL Classification

  • C61
  • C70
  • D44