Truth, Envy, and Truthful Market Clearing Bundle Pricing

  • Edith Cohen
  • Michal Feldman
  • Amos Fiat
  • Haim Kaplan
  • Svetlana Olonetsky
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7090)

Abstract

We give a non-trivial class of valuation functions for which we give auctions that are efficient, truthful and envy-free.

We give interesting classes of valuations for which one can design such auctions. Surprisingly, we also show that minor modifications to these valuations lead to impossibility results, the most surprising of which is that for a natural class of valuations, one cannot achieve efficiency, truthfulness, envy freeness, individual rationality, and no positive transfers.

We also show that such auctions also imply a truthful mechanism for computing bundle prices (“shrink wrapped” bundles of items), that clear the market. This extends the class of valuations for which truthful market clearing prices mechanisms exist.

Keywords

Incentive Compatible Valuation Function Combinatorial Auction Positive Transfer Walrasian Equilibrium 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ausubel, L., Milgrom, P.: Ascending auctions with package bidding. Frontiers of Theoretical Economics 1, 1–42 (2002)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Blumrosen, L., Nisan, N.: Combinatorial auctions. In: Tardos, E., Vazirani, V., Nisan, N., Roughgarden, T. (eds.) Algorithmic Game Theory. Cambridge University Press (2007)Google Scholar
  3. 3.
    Blumrosen, L., Nisan, N.: Informational limitations of ascending combinatorial auctions. Journal of Economic Theory 145, 1203–1223 (2001)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Clarke, E.: Multipart Pricing of Public Goods. Public Choice 1, 17–33 (1971)CrossRefGoogle Scholar
  5. 5.
    Cohen, E., Feldman, M., Fiat, A., Kaplan, H., Olonetsky, S.: On the Interplay between Incentive Compatibility and Envy Freeness, http://arxiv.org/abs/1003.5328
  6. 6.
    Dubins, L.E., Spanier, E.H.: How to cut a cake fairly. American Mathematical Monthly (1961)Google Scholar
  7. 7.
    Foley, D.: Resource allocation and the public sector. Yale Economic Essays 7, 45–98 (1967)Google Scholar
  8. 8.
    Fleischer, L., Wang, Z.: Lower Bound for Envy-Free and Truthful Makespan Approximation on Related Machines. In: Persiano, G. (ed.) SAGT 2011. LNCS, vol. 6982, pp. 166–177. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  9. 9.
    Demange, G., Gale, D., Sotomayor, M.: Multi-Item Auctions. Journal of Political Economy (1986)Google Scholar
  10. 10.
    Gul, F., Stacchetti, E.: Walrasian equilibrium with gross substitutes. Journal of Economic Theory 87, 95–124 (1999)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Hurwicz, L.: Optimality and informational efficiency in resource allocation processes. In: Arrow, K.J., Karlin, S., Suppes, P. (eds.) Mathematical Methods in the Social Sciences (1960)Google Scholar
  12. 12.
    Kelso, A., Crawford, V.: Job Matching, Coalition Formation, and Gross Substitutes. Econometrica (1982)Google Scholar
  13. 13.
    Lehmann, B., Lehmann, D.J., Nisan, N.: Combinatorial Auctions with Decreasing Marginal Utilities. In: ACM Conference on Electronic Commerce (2001)Google Scholar
  14. 14.
    Leonard, H.B.: Elicitation of honest preferences for the assignment of individuals to positions. The Journal of Political Economy 91(3), 461–479 (1983)CrossRefGoogle Scholar
  15. 15.
    Maskin, E.S.: On the fair allocation of indivisible goods. In: Feiwel, G. (ed.) Arrow and the Foundations of the Theory of Economic Policy (essays in honor of Kenneth Arrow) (1987)Google Scholar
  16. 16.
    Moulin, H.: Fair Division and Collective Welfare. MIT Press (2004)Google Scholar
  17. 17.
    Nisan, N.: Introduction to mechanism design. In: Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V. (eds.) Algorithmic Game Theory. Cambridge University Press (2007)Google Scholar
  18. 18.
    Pápai, S.: Groves sealed bid auctions of heterogeneous objects with fair prices. Social choice and Welfare 20, 371–385 (2003)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Parkes, D.: Iterative combinatorial auctions: Achieving economic and computational effciency. Ph.D. Thesis, Department of Computer and Information Science, University of Pennsylvania (2001)Google Scholar
  20. 20.
    Pulleyblank, W.: Dual integrality in b-matching problems. In: Cottle, R.W., et al. (eds.) Combinatorial Optimization. Mathematical Programming Studies, vol. 12 (1980)Google Scholar
  21. 21.
    Raz, D., Levy, H., Avi-Itzhak, B.: A resource-allocation queueing fairness measure. In: SIGMETRICS (2004)Google Scholar
  22. 22.
    Svensson, L.G.: On the existence of fair allocations. Journal of Economics (1983)Google Scholar
  23. 23.
    Vickrey, W.: Counterspeculation, Auctions, and Competitive Sealed Tenders. Journal of Finance (1961)Google Scholar
  24. 24.
    Young, H.P.: Equity: In Theory and Practice. Princeton University Press (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Edith Cohen
    • 1
  • Michal Feldman
    • 2
  • Amos Fiat
    • 3
  • Haim Kaplan
    • 3
  • Svetlana Olonetsky
    • 3
  1. 1.AT&T Labs-ResearchFlorham ParkIsrael
  2. 2.School of Business AdministrationThe Hebrew University of JerusalemIsrael
  3. 3.The Blavatnik School of Computer ScienceTel Aviv UniversityIsrael

Personalised recommendations