An average lexicographic value for cooperative games

S.H. Tijs, P.E.M. Borm, E.R.M.A. Lohmann, M. Quant

Research output: Contribution to journalArticleScientificpeer-review

Abstract

For games with a non-empty core the Alexia value is introduced, a value which averages the lexicographic maxima of the core. It is seen that the Alexia value coincides with the Shapley value for convex games, and with the nucleolus for strongly compromise admissible games and big boss games. For simple flow games, clan games and compromise stable games an explicit expression and interpretation of the Alexia value is derived. Furthermore it is shown that the reverse Alexia value, defined by averaging the lexicographic minima of the core, coincides with the Alexia value for convex games and compromise stable games.
Original languageEnglish
Pages (from-to)210-220
JournalEuropean Journal of Operational Research
Volume213
Issue number1
DOIs
Publication statusPublished - 2011

Fingerprint

Cooperative Game
Game
Convex Games
Nucleolus
Shapley Value
Cooperative game
Averaging
Reverse
Compromise

Keywords

  • game theory
  • Alexia value
  • convexity
  • comprise stability
  • big boss and clan games

Cite this

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title = "An average lexicographic value for cooperative games",
abstract = "For games with a non-empty core the Alexia value is introduced, a value which averages the lexicographic maxima of the core. It is seen that the Alexia value coincides with the Shapley value for convex games, and with the nucleolus for strongly compromise admissible games and big boss games. For simple flow games, clan games and compromise stable games an explicit expression and interpretation of the Alexia value is derived. Furthermore it is shown that the reverse Alexia value, defined by averaging the lexicographic minima of the core, coincides with the Alexia value for convex games and compromise stable games.",
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An average lexicographic value for cooperative games. / Tijs, S.H.; Borm, P.E.M.; Lohmann, E.R.M.A.; Quant, M.

In: European Journal of Operational Research, Vol. 213, No. 1, 2011, p. 210-220.

Research output: Contribution to journalArticleScientificpeer-review

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AU - Tijs, S.H.

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AU - Quant, M.

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KW - game theory

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KW - convexity

KW - comprise stability

KW - big boss and clan games

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