Social Choice and Welfare

, Volume 34, Issue 2, pp 193–216 | Cite as

Auctioning or assigning an object: some remarkable VCG mechanisms

Original Paper

Abstract

We construct a variant of the Vickrey auction of a single object where the surplus is split in exogenously fixed shares between the seller and the buyers, up to a margin of error vanishingly exponentially as the number of buyers grows. When the object is the common property of the participants, we can similarly construct VCG mechanisms with a vanishingly small cash transfer to the residual claimant. For any integer q, 3 ≤ q ≤ n, we find the mechanism guaranteeing to each participant a fair share of the qth highest valuation, while minimizing the worst possible ratio of the cash transfer to the efficient surplus. We perform a parallel analysis when the object is undesirable. We compare the cash lost to the largest spread between individual valuations, and obtain the same trade-offs between fairness and the relative loss of surplus.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alkan A, Demange G, Gale D (1991) Fair allocation of indivisible goods and criteria of justice. Econometrica 59: 1023–1039CrossRefGoogle Scholar
  2. Ando K, Kato M, Ohseto S (2008) Strategy-proof and symmetric allocation of an indivisible good. Math Soc Sci 55(1): 14–23Google Scholar
  3. Aragones E (1995) A derivation of the money Rawlsian solution. Soc Choice Welf 12: 267–276CrossRefGoogle Scholar
  4. Atlamaz M, Yengin D (2006) Fair Groves mechanisms. Rochester University, MimeoGoogle Scholar
  5. Bailey MJ (1997) The demand revealing process: to distribute the surplus. Public Choice 91: 107–126CrossRefGoogle Scholar
  6. Cavallo R (2006) Optimal decision-making with minimal waste: strategyproof redistribution of VCG payments. International Conference on Autonomous Agents and Multi-agents Systems (AAMAS), Hakodate, JapanGoogle Scholar
  7. Cramton P, Gibbons R, Klemperer P (1987) Dissolving a partnership efficiently. Econometrica 55(3): 615–632CrossRefGoogle Scholar
  8. Guo M, Conitzer V (2007) Worst case optimal redistribution of VCG payments. Conference on Electronic Commerce (EC), San Diego, June 2007Google Scholar
  9. Green J, Laffont JJ (1979) Incentives in public decision making. North-Holland, AmsterdamGoogle Scholar
  10. Holmstrom B (1979) Groves’ schemes on restricted domains. Econometrica 47: 1137–1144CrossRefGoogle Scholar
  11. Johari R, Tsitsiklis J (2004) Efficiency loss in a network resource allocation game. Math Oper Res 29(3): 407–435CrossRefGoogle Scholar
  12. Klijn F (2000) An algorithm for envy-free allocations in an economy with indivisibles objects and money. Soc Choice Welf 17: 201–215CrossRefGoogle Scholar
  13. Koutsoupias E, Papadimitriou C (1999) Worst case equilibria. In: Proceedings of the 16th Symposium on Theoretical Aspects of Computer Science, pp 404–413Google Scholar
  14. Kunreuther H (1996) The role of compensation in siting hazardous facilities. J Policy Anal Manage 15(3): 601–622CrossRefGoogle Scholar
  15. Moulin H (1986) Characterizations of the pivotal mechanism. J Public Econ 31: 53–78CrossRefGoogle Scholar
  16. Moulin H (1992) An application of the shapley value to fair division with money. Econometrica 60(6): 1331–1349CrossRefGoogle Scholar
  17. Moulin H (2009) Efficient strategy-proof and almost budget-balanced assignment. J Econ Theory 144: 96–119CrossRefGoogle Scholar
  18. Moulin H (2008) The price of anarchy of serial, average and incremental cost sharing. Econ Theory 36: 379–405CrossRefGoogle Scholar
  19. Ohseto S (2006) Characterizations of strategy-proof and fair mechanisms for allocating indivisible goods. Econ Theory 29(1): 111–121CrossRefGoogle Scholar
  20. Papai S (2003) Groves sealed bid auctions of heterogenous objects with fair prices. Soc Choice Welf 20(3): 371–386CrossRefGoogle Scholar
  21. Porter R, Shoham Y, Tennenholtz M (2004) Fair imposition. J Econ Theory 118: 209–228CrossRefGoogle Scholar
  22. Roughgarden T, Tardos E (2002) Bad is selfish routing. J ACM 49(2): 236–259CrossRefGoogle Scholar
  23. Tennenholtz M (2001) Rational competitive analysis. In: Proceedings of IJCAI-01Google Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.HoustonUSA

Personalised recommendations