Mechanisms and Impossibilities for Truthful, Envy-Free Allocations

  • Michal Feldman
  • John Lai
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7615)


We study mechanisms for combinatorial auctions that are simultaneously incentive compatible (IC), envy free (EF) and efficient in settings with capacitated valuations — a subclass of subadditive valuations introduced by Cohen et al. [4]. Capacitated agents have valuations which are additive up to a publicly known capacity. The main result of Cohen et al. [4] is the assertion that the Vickrey-Clarke-Groves mechanism with Clarke pivot payments is EF (and clearly IC and efficient) in the case of homogeneous capacities. The main open problem raised by Cohen et al. [4] is whether the existence result extends beyond homogeneous capacities. We resolve the open problem, establishing that no mechanism exists that is simultaneously IC, EF and efficient for capacitated agents with heterogeneous capacities. In addition, we establish the existence of IC, EF, and efficient mechanisms in the special cases of capacitated agents with heterogeneous capacities, where (i) there are only two items; or (ii) the individual item values are binary. Finally, we show that the last existence result does not extend to the stronger notion of Walrasian mechanisms, i.e. mechanisms whose allocation and payments correspond to a Walrasian equilibrium.


Incentive Compatibility Valuation Function Combinatorial Auction Walrasian Equilibrium Payment Rule 
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.
    Ausubel, L.M., Milgrom, P.: The lovely but lonely vickrey auction. In: Combinatorial Auctions, ch. 1. MIT Press (2006)Google Scholar
  2. 2.
    Bikhchandani, S., Ostroy, J.: The package assignment model. Journal of Economic Theory 107(2), 377–406 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Clarke, E.H.: Multipart pricing of public goods. Public Choice, 17–33 (1971)Google Scholar
  4. 4.
    Cohen, E., Feldman, M., Fiat, A., Kaplan, H., Olonetsky, S.: Truth, Envy, and Truthful Market Clearing Bundle Pricing. In: Chen, N., Elkind, E., Koutsoupias, E. (eds.) WINE 2011. LNCS, vol. 7090, pp. 97–108. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  5. 5.
    Dubins, L.E., Spanier, E.H.: How to cut a cake fairly. The American Mathetmatical Monthly 68(1), 1–17 (1961)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Foley, D.K.: Resource allocation and the public sector. Yale Economic Studies (1967)Google Scholar
  7. 7.
    Green, J., Laffont, J.: Characterization of satisfactory mechanisms for the revelation of preferences for public goods. Econometrica 45(2), 427–438 (1973)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Groves, T.: Incentives in teams. Econometrica 41(4), 617–631 (1973)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Gul, F., Stacchetti, E.: Walrasian equilibrium with gross substitutes. Journal of Economic Theory 87, 95–124 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Holmstrom, B.: Groves schemes on restricted domains. Econometrica 47(5), 1137–1144 (1979)CrossRefMathSciNetGoogle 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. Stanford University Press (1960)Google Scholar
  12. 12.
    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
  13. 13.
    Maskin, E.S.: On the fair allocation of indivisible goods (1987)Google Scholar
  14. 14.
    Moulin, H.: Fair Division and Collective Welfare. MIT Press (2004)Google Scholar
  15. 15.
    Mu’alem, A.: On Multi-dimensional Envy-Free Mechanisms. In: Rossi, F., Tsoukias, A. (eds.) ADT 2009. LNCS, vol. 5783, pp. 120–131. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  16. 16.
    Pápai, S.: Groves sealed bid auctions of heterogeneous objects with fair prices. Social Choice and Welfare 20(3), 371–385 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Rafaeli, A., Kedmi, E., Vashdi, D., Barron, G.: Queues and fairness: A multiple study experimental investigation. Technical report, Technion-Israel Institute of Technology (2003)Google Scholar
  18. 18.
    Svensson, L.: On the existence of fair allocations. Journal of Economics 43(3), 301–308 (1983)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Michal Feldman
    • 1
    • 2
  • John Lai
    • 1
  1. 1.Harvard School of Engineering and Applied SciencesCambridgeUSA
  2. 2.Hebrew University of JerusalemJerusalemIsrael

Personalised recommendations