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URN: urn:nbn:de:0030-drops-12312
URL: http://drops.dagstuhl.de/opus/volltexte/2007/1231/

Moulin, Hervé

Efficient cost sharing with a cheap residual claimant

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Abstract

For the cooperative production problem where the commons is a one dimensional convex cost function, I propose the residual mechanism to implement the efficient production level . In contrast to the familiar cost sharing methods such as serial, average and incremental, the residual mechanism may subsidize an agent with a null demand. IFor a large class of smooth cost functions, the residual mechanism generates a budget surplus that is, even in the worst case, vanishes as 1/logn where n is the number of participants. Compare with the serial, average and incremental mechanisms, of which the budget surplus, in the worst case, converges to the efficient surplus as n grows. The second problem is the assignment among n agents of p identical objects and cash transfers to compensate the losers. We assume p<n, and compute the optimal competitive performance among all VCG mechanisms generating no budget deficit. It goes to zero exponentially fast in n if the number of objects is fixed; and as (n)^(1/2) uniformly in p. The mechanism generates envy, and net utilities are not co-monotonic to valuations. When p>n/2, it may even fail to achieve voluntary participation.

BibTeX - Entry

@InProceedings{moulin:DSP:2007:1231,
  author =	{Herv{\'e} Moulin},
  title =	{Efficient cost sharing with a cheap residual claimant},
  booktitle =	{Fair Division},
  year =	{2007},
  editor =	{Steven Brams and Kirk Pruhs and Gerhard Woeginger},
  number =	{07261},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2007/1231},
  annote =	{Keywords: Assignment, cost sharing, Vickrey-Clarke-Groves mechanisms, competitive analysis}
}

Keywords: Assignment, cost sharing, Vickrey-Clarke-Groves mechanisms, competitive analysis
Seminar: 07261 - Fair Division
Issue date: 2007
Date of publication: 26.11.2007


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