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pp 1–32 | Cite as

Evaluating groups with the generalized Shapley value

  • Ramón Flores
  • Elisenda Molina
  • Juan Tejada
Research Paper
  • 43 Downloads

Abstract

Following the original interpretation of the Shapley value as a priori evaluation of the prospects of a player in a multi-person interaction situation, we intend to apply the Shapley generalized value (introduced formally in Marichal et al. in Discrete Appl Math 155:26–43, 2007) as a tool for the assessment of a group of players that act as a unit in a coalitional game. We propose an alternative axiomatic characterization which does not use a direct formulation of the classical efficiency property. Relying on this valuation, we also analyze the profitability of a group. We motivate this use of the Shapley generalized value by means of two relevant applications in which it is used as an objective function by a decision maker who is trying to identify an optimal group of agents in a framework in which agents interact and the attained benefit can be modeled by means of a transferable utility game.

Keywords

Game theory TU games Shapley value Generalized values Group values 

Mathematics Subject Classification

91A12 91A43 

Notes

Acknowledgements

We would like to warmly thank Javier Castro (Universidad Complutense de Madrid) for the simulation program used to obtain the numerical results in Sect. 5.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de Geometría y TopologíaIMUS-Universidad de SevillaSevilleSpain
  2. 2.Departamento de EstadísticaUniversidad Carlos III de MadridMadridSpain
  3. 3.Departamento de Estadística e Investigación Operativa, Instituto de Matemática Interdisciplinar (IMI)Universidad Complutense de MadridMadridSpain

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