Review of Economic Design

, Volume 21, Issue 1, pp 1–31 | Cite as

Mechanisms for combinatorial auctions with budget constraints

Original Paper
  • 151 Downloads

Abstract

This paper studies combinatorial auctions with budget-constrained bidders from a mechanism design perspective. I search for mechanisms that are incentive compatible, individually rational, symmetric, non-wasteful and non-bossy. First focusing on the greedy domain, in which any increase in a bidder’s valuation always exceeds his budget, I derive the unique mechanism, called the Iterative Second Price Auction. For the general domain, however, no such mechanism exists.

Keywords

Combinatorial auctions Budget constraints Mechanisms 

JEL Classification

D44 D82 

Notes

Acknowledgments

I want to thank Fuhito Kojima, Ilya Segal, Alex Wolitzky and Gabriel Carroll for their helpful comments on a version of this paper that was in my dissertation at Stanford University, and am grateful to two anonymous referees for their insightful comments.

References

  1. Ausubel LM (2004) An efficient ascending-bid auction for multiple objects. Am Econ Rev 94(5):1452–1475Google Scholar
  2. Bhattacharya S, Conitzer V, Munagala K, Xia L (2010) Incentive compatible budget elicitation in multi-unit auctions. In: Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms, pp 554–572. Society for Industrial and Applied MathematicsGoogle Scholar
  3. Borgs C, Chayes J, Immorlica N, Mahdian M, Saberi A (2005) Multi-unit auctions with budget-constrained bidders. In: Proceedings of the 6th ACM conference on electronic commerce, pp 44–51. ACMGoogle Scholar
  4. Bulow J, Levin J, Milgrom P (2009) Winning play in spectrum auctions. Technical report, National Bureau of Economic ResearchGoogle Scholar
  5. Che Y-K, Gale I (1996) Expected revenue of all-pay auctions and first-price sealed-bid auctions with budget constraints. Econ Lett 50(3):373–379CrossRefGoogle Scholar
  6. Che Y-K, Gale I (2000) The optimal mechanism for selling to a budget-constrained buyer. J Econ Theory 92(2):198–233CrossRefGoogle Scholar
  7. Day R, Milgrom P (2008) Core-selecting package auctions. Int J Game Theory 36(3–4):393–407CrossRefGoogle Scholar
  8. Dobzinski S, Lavi R, Nisan N (2012) Multi-unit auctions with budget limits. Games Econ Behav 74(2):486–503CrossRefGoogle Scholar
  9. Dughmi S, Vondrák J (2015) Limitations of randomized mechanisms for combinatorial auctions. Games Econ Behav 92:370–400Google Scholar
  10. Fiat A, Leonardi S, Saia J, Sankowski P (2011) Single valued combinatorial auctions with budgets. In: Proceedings of the 12th ACM conference on electronic commerce, pp 223–232. dACMGoogle Scholar
  11. Goel G, Mirrokni V, Paes Leme R (2012) Polyhedral clinching auctions and the adwords polytope. In: Proceedings of the forty-fourth annual ACM symposium on Theory of computing, pp 107–122. ACMGoogle Scholar
  12. Hafalir IE, Ravi R, Sayedi A (2012) A near Pareto optimal auction with budget constraints. Games Econ Behav 74(2):699–708CrossRefGoogle Scholar
  13. Laffont J-J, Robert J (1996) Optimal auction with financially constrained buyers. Econ Lett 52(2):181–186CrossRefGoogle Scholar
  14. Lavi R, May M (2012) A note on the incompatibility of strategy-proofness and pareto-optimality in quasi-linear settings with public budgets. Econo Lett 115(1):100–103CrossRefGoogle Scholar
  15. Milgrom P (2000) Putting auction theory to work: the simultaneous ascending auction. J Polit Econ 108(2):245–272CrossRefGoogle Scholar
  16. Milgrom P, Segal I (2014) Deferred-acceptance auctions and radio spectrum reallocation. In: Proceedings of the fifteenth ACM conference on economics and computation, pp 185–186. ACMGoogle Scholar
  17. Nisan N, Ronen A (2007) Computationally feasible VCG mechanisms. J Artif Intell Res 29:19–47Google Scholar
  18. Satterthwaite MA, Sonnenschein H (1981) Strategy-proof allocation mechanisms at differentiable points. Rev Econ Stud 48(4):587–597Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Stanford UniversityStanfordUSA

Personalised recommendations