Shapley’s Axiomatics for Lexicographic Cooperative Games

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Author(s)

Guram N. Beltadze 1,* Jimsher A. Giorgobiani 2

1. Departments Control Systems and Mathematics, Georgian Technical University, Georgia, Tbilisi, 0175, str. Kostava 77

2. N. Muskhelishvili Institute of Computational Mathematics, Georgian Technical University, Tbilisi, 0175, str. Kostava 77

* Corresponding author.

DOI: https://doi.org/10.5815/ijmecs.2015.08.01

Received: 23 Apr. 2015 / Revised: 5 Jun. 2015 / Accepted: 1 Jul. 2015 / Published: 8 Aug. 2015

Index Terms

Game, Lexicography, Cooperative Game, Shapley’s axiomatics, Matrixs of distribution

Abstract

In classical cooperative game theory one of the most important principle is defined by Shapley with three axioms common payoff fair distribution’s Shapley value (or Shapley vector). In the last decade the field of its usage has been spread widely. At this period of time Shapley value is used in network and social systems. Naturally, the question is if it is possible to use Shapley’s classical axiomatics for lexicographic cooperative games. Because of this in the article for dimensional lexicographic cooperative game is introduced Shapley’s axiomatics, as the principle of a fair distribution in the case of dimensional payoff functions, when the criteria are strictly ranking. It has been revealed that axioms discussed by Shapley for classical games are sufficient in lexicographic cooperative games corresponding with the payoffs of distribution. Besides we are having a very interesting case: according to the proved theorem, Shapley’s classical principle simultaneously transforms on the composed scalar games of a lexicographic cooperative game, nevertheless, games could not be superadditive.

Cite This Paper

Guram N. Beltadze, Jimsher A. Giorgobiani, "Shapley's Axiomatics for Lexicographic Cooperative Games", International Journal of Modern Education and Computer Science (IJMECS), vol.7, no.8, pp.1-8, 2015. DOI:10.5815/ijmecs.2015.08.01

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