Geometric Study of the Weak Equilibrium in a Weighted Case for a Two-Dimensional Competition Game

López M. Dolores, Rodrigo Javier, Sánchez José Manuel

Departamento de Matemática Aplicada de la E.T.S.I. Caminos, Canales y Puertos.
Departamento de Matemática Aplicada de la E.T.S.I. Caminos, Canales y Puertos..
Departamento de Matemática Aplicada, E.T.S. de Ingeniería, Universidad Pontificia Comillas de Madrid, Madrid, Spain.

DOI: 10.4236/ajor.2013.33030                

Abstract

In this work, an improvement of the results presented by [1] Abellanas et al. (Weak Equilibrium in a Spatial Model. International Journal of Game Theory, 40(3), 449-459) is discussed. Concretely, this paper investigates an abstract game of competition between two players that want to earn the maximum number of points from a finite set of points in the plane. It is assumed that the distribution of these points is not uniform, so an appropriate weight to each position is assigned. A definition of equilibrium which is weaker than the classical one is included in order to avoid the uniqueness of the equilibrium position typical of the Nash equilibrium in these kinds of games. The existence of this approximated equilibrium in the game is analyzed by means of computational geometry techniques.

Keywords

Game Theory; Approximated Equilibrium; Location; Computational Geometry; Convex Hull

Conflicts of Interest

The authors declare no conflicts of interest.

References

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