A Value for Graph-Restricted Games with Middlemen on Edges

Antonio C. Alarcón, José M. Gallardo and Andrés Jiménez-Losada
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Antonio C. Alarcón: Departamento de Ciencias Integradas, Facultad de Ciencias Experimentales, Universidad de Huelva, 21007 Huelva, Spain
José M. Gallardo: Departamento de Matemática Aplicada II, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, 41092 Sevilla, Spain
Andrés Jiménez-Losada: Departamento de Matemática Aplicada II, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, 41092 Sevilla, Spain

Mathematics, 2022, vol. 10, issue 11, 1-15

Abstract: In a cooperative game with a communication structure, a graph describes the communication possibilities of the players, which are represented by the nodes. We introduce a variation of this model by assuming that each edge in the communication graph represents an agent. These agents simply act as intermediaries, but since they are essential for the cooperation and, consequently, for revenue generation, they will claim their share of the profit. We study this new model of games with a communication structure and introduce an allocation rule for these games. The motivation for analyzing this type of problem is based on the construction of a risk index for the different elements of an internal network.

Keywords: cooperative game; Shapley value; restricted cooperation; graph-restricted game; Myerson value (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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