Leximals, the Lexicore and the Average Lexicographic Value

Y. Funaki, S.H. Tijs, R. Brânzei

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Abstract

The lexicographic vectors of a balanced game, called here leximals, are used to define a new solution concept, the lexicore, on the cone of balanced games. Properties of the lexicore and its relation with the core on some classes of games are studied. It is shown that on cones of balanced games where the core is additive, the leximals, the lexicore and the Average Lexicographic (AL-)value are additive, too. Further, it turns out that the leximals satisfy a consistency property with respect to a reduced game `a la Davis and Maschler, which implies an average consistency property of the AL-value. Explicit formulas for the AL-value on the class of k-convex games and on the class of balanced almost convex games are provided.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages23
Volume2007-97
Publication statusPublished - 2007

Publication series

NameCentER Discussion Paper
Volume2007-97

Keywords

  • cooperative games
  • the core
  • the AL-value
  • the Shapley value

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    Funaki, Y., Tijs, S. H., & Brânzei, R. (2007). Leximals, the Lexicore and the Average Lexicographic Value. (CentER Discussion Paper; Vol. 2007-97). Operations research.