On the computation of the nucleolus of a cooperative game

U Faigle*, W Kern, J Kuipers

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

We consider classes of cooperative games. We show that we can efficiently compute an allocation in the intersection of the prekernel. and the least core of the game if we can efficiently compute the minimum excess for any given allocation. In the case where the prekernel of the game contains exactly one core vector, our algorithm computes the nucleolus of the game. This generalizes both a recent result by Kuipers on the computation of the nucleolus for convex games and a classical result by Megiddo on the nucleolus of standard tree games to classes of more general minimum cost spanning tree games. Our algorithm is based on the ellipsoid method and Maschler's scheme for approximating the prekernel.

Original languageEnglish
Pages (from-to)79-98
Number of pages20
JournalInternational Journal of Game Theory
Volume30
Issue number1
DOIs
Publication statusPublished - Sep 2001

Keywords

  • core
  • nucleolus
  • prekernel
  • kernel
  • computational complexity
  • convex games
  • MCST-games
  • ellipsoid method
  • SPANNING TREE GAMES
  • COST ALLOCATION
  • COMPLEXITY
  • ALGORITHM
  • TIME
  • CORE

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