The Family of Lattice Structure Values for Games with Externalities

UB Economics working Papers E18/379

32 Pages Posted: 26 Sep 2018

See all articles by José María Alonso-Meijide

José María Alonso-Meijide

Universidade de Santiago de Compostela

Mikel Alvarez-Mozos

University of Barcelona - Department of Actuarial, Financial and Economic Mathematics

M. Gloria Fiestras-Janeiro

University of Vigo

Andres Jimenez-Losada

University of Seville

Date Written: July 29, 2018

Abstract

We propose and characterize a new family of Shapley values for games with coalitional externalities. To define it we generalize the concept of marginal contribution by using a lattice structure on the set of embedded coalitions. The family of lattice structure values is characterized by extensions of Shapley's axioms: efficiency, additivity, symmetry, and the null player property. The first three axioms have widely accepted generalizations to the framework of games with externalities. However, different concepts of null players have been proposed in the literature and we contribute to this debate with a new one. The null player property that we use is weaker than the others. Finally, we present one particular value of the family, new in the literature, which delivers balanced payoffs and characterize it by two additional properties.

Keywords: Externalities, Partition Function, Basis, Lattice, Marginal Contribution

JEL Classification: C71

Suggested Citation

Alonso-Meijide, José María and Alvarez-Mozos, Mikel and Fiestras-Janeiro, M. Gloria and Jimenez-Losada, Andres, The Family of Lattice Structure Values for Games with Externalities (July 29, 2018). UB Economics working Papers E18/379, Available at SSRN: https://ssrn.com/abstract=3244403 or http://dx.doi.org/10.2139/ssrn.3244403

José María Alonso-Meijide (Contact Author)

Universidade de Santiago de Compostela ( email )

Complejo Docente - Campus Universitario de Lugo
Lugo, A Coruña 15704
Spain

Mikel Alvarez-Mozos

University of Barcelona - Department of Actuarial, Financial and Economic Mathematics ( email )

Avda. Diagonal 690
Barcelona, 08034
Spain

M. Gloria Fiestras-Janeiro

University of Vigo ( email )

Campus Universitario Lagoas-Marcosende
Vigo, 36200
Spain

Andres Jimenez-Losada

University of Seville

Sevilla
Spain

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