abstract

• The Myerson value is a characterized allocation rule for analyzing games with a coalitional structure, merging ideas from graph theory and classical cooperative game theory. In this article, we extend these ideas to characterize a solution for cooperative interval games, which consist of a finite set of players, where the coalition values are compact intervals of real numbers. We adapt the axiom of efficiency by connected components, which Myerson proposed in the classical theory of cooperative games with graphs, to interval games. Additionally, we introduce the concept of superadditivity under τ and define a new axiom, which we call equity with respect to τ. With these two properties, we propose a new characterization of the interval Myerson value.

authors

• Olvera López William José

publication date

• 2025-01-01

funding provided via

• Consejo Nacional de Humanidades, Ciencias y Tecnologías, Conahcyt  Grant

published in

• Journal of Dynamics and Games  Journal

keywords

• allocation rule; cooperative interval game; cooperative structures; Graph theory; size monotonic games Game theory; Allocation rule; Coalition value; Cooperative game theory; Cooperative interval game; Cooperative structure; Finite set; Monotonics; Myerson value; Real number; Size monotonic game; Graph theory

Digital Object Identifier (DOI)

• 10.3934/jdg.2024018

PubMed ID

start page

• 157

end page

• 168

volume

• 12

issue

• 2