Operations-Research-Spektrum

, Volume 6, Issue 2, pp 119–123 | Cite as

Permutation games: Another class of totally balanced games

  • S. H. Tijs
  • T. Parthasarathy
  • J. A. M. Potters
  • V. Rajendra Prasad
Theoretical Papers

Summary

A class of cooperative games in characteristic function form arising from certain sequencing problems and assignment problems, is introduced. It is shown that games of this class are totally balanced. In the proof of this fact we use the Birkhoff-von Neumann theorem on doubly stochastic matrices and the Bondareva-Shapley theorem on balanced games. It turns out that this class of permutation games coincides with the class of totally balanced games if the number of players is smaller than four. For larger games the class of permutation games is a nonconvex subset of the convex cone of totally balanced games.

Keywords

Characteristic Function Assignment Problem Convex Cone Function Form Cooperative Game 

Zusammenfassung

Wir führen eine Klasse von kooperativen Spielen in charakteristischer Funktionsform ein, die bei gewissen Folgeproblemen und Zuordnungsproblemen auftreten. Wir zeigen, daß diese Spiele vollständig balanciert sind. Zum Beweis verwenden wir den Satz von Birkhoff-von Neumann über doppelt stochastische Matrizen und den Satz von Bondareva-Shaplex über balancierte Spiele. Es zeigt sich, daß diese Klasse von Permutationsspielen mit der Klasse von vollständig balancierten Spiele übereinstimmt, falls die Zahl der Spieler kleiner als vier ist. Für größere Spiele ist die Klasse der Permutationsspiele eine nichtkonvexe Teilmenge des konvexen Kegels der vollständig balancierten Spiele.

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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • S. H. Tijs
    • 1
  • T. Parthasarathy
    • 2
  • J. A. M. Potters
    • 1
  • V. Rajendra Prasad
    • 2
  1. 1.Department of MathematicsCatholic UniversityED NijmegenThe Netherlands
  2. 2.Indian Statistical InstituteNew DelhiIndia

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