Nonatomic Non-Cooperative Neighbourhood Balancing Games

Issue title: Codes, Graphs, Coverings, and Identification: Special Issue Honoring the 60-th Birthday of Professor Iiro Honkala

Guest editors: Vesa Halava, Jarkko Kari and Tero Laihonen

Article type: Research Article

Authors: Auger, David^{a; *; †} | Cohen, Johanne^{b; ‡} | Lobstein, Antoine^c

Affiliations: [a] Université Paris-Saclay, UVSQ, DAVID, 78035, Versailles, France. david.auger@uvsq.fr | [b] Université Paris-Saclay, CNRS, LISN, 91405, Orsay, France. Johanne.Cohen@universite-paris-saclay.fr | [c] Université Paris-Saclay, CNRS, LISN, 91405, Orsay, France. Antoine.Lobstein@lri.fr

Correspondence: [*] Address for correspondence: Université Paris-Saclay, UVSQ, DAVID, 78035, Versailles, France.

Note: [†] This work was supported by a public grant as part of the Investissement d’avenir project, reference ANR-11-LABX-0056-LMH, LabEx LMH.

Note: [‡] idem

Abstract: We introduce a game where players selfishly choose a resource and endure a cost depending on the number of players choosing nearby resources. We model the influences among resources by a weighted graph, directed or not. These games are generalizations of well-known games like Wardrop and congestion games. We study the conditions of equilibria existence and their efficiency if they exist. We conclude with studies of games whose influences among resources can be modelled by simple graphs.

Keywords: Neighbourhood Balancing Games, Nash equilibrium, graph theory

DOI: 10.3233/FI-242181

Journal: Fundamenta Informaticae, vol. 191, no. 3-4, pp. 239-268, 2024