A New Characterization of the Pre-Kernel for TU Games Through its Indirect Function and its Application to Determine the Nucleolus for Three Subclasses of TU Games

Authors

  • Dongshuang Hou University of Twente
  • Theo Driessen University of Twente
  • Antoni Meseguer-Artola Universitat Oberta de Catalunya
  • Boglárka Mosoni Babes-Bolyai University

Abstract

The main goal is twofold. Thanks to the so-called indirect function
known as the dual representation of the characteristic function of a
coalitional TU game, we derive a new characterization of the pre-kernel of
the coalitional game using the evaluation of its indirect function on the tails
of pairwise bargaining ranges arising from a given payoff vector. Secondly,
we study three subclasses of coalitional games of which its indirect function
has an explicit formula and show the applicability of the determination of
the pre-kernel (nucleolus) for such types of games using the indirect function.
Three such subclasses of games concern the 1−convex and 2-convex n
person games and clan games. A clan game with the clan to be s singleton
is known as a big boss game.

Keywords:

dual representation, indirect function, pre-kernel, 1- and 2- convex n person games, clan games, big boss games

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References

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Published

2022-08-18

How to Cite

Hou, D. ., Driessen, T., Meseguer-Artola, A., & Mosoni, B. (2022). A New Characterization of the Pre-Kernel for TU Games Through its Indirect Function and its Application to Determine the Nucleolus for Three Subclasses of TU Games. Contributions to Game Theory and Management, 6. Retrieved from https://gametheory.spbu.ru/article/view/14208

Issue

Vol. 6 (2013)

Section

Articles

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Articles of "Contributions to Game Theory and Management" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.