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

López González, M. Dolores and Rodrigo Hitos, Javier and Sánchez, José Manuel (2013). Geometric Study of the Weak Equilibrium in a Weighted Case for a Two-Dimensional Competition Game. "American Journal of Operations Research", v. 3 (n. 3); pp. 337-341. ISSN 2160-8830. https://doi.org/10.4236/ajor.2013.33030.

Description

Title: Geometric Study of the Weak Equilibrium in a Weighted Case for a Two-Dimensional Competition Game
Author/s:
  • López González, M. Dolores
  • Rodrigo Hitos, Javier
  • Sánchez, José Manuel
Item Type: Article
Título de Revista/Publicación: American Journal of Operations Research
Date: 23 May 2013
ISSN: 2160-8830
Volume: 3
Subjects:
Freetext Keywords: Game Theory; Approximated Equilibrium; Location; Computational Geometry; Convex Hull
Faculty: E.T.S.I. Caminos, Canales y Puertos (UPM)
Department: Matemática e Informática Aplicadas a la Ingeniería Civil [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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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.

More information

Item ID: 33236
DC Identifier: http://oa.upm.es/33236/
OAI Identifier: oai:oa.upm.es:33236
DOI: 10.4236/ajor.2013.33030
Official URL: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=31666
Deposited by: Memoria Investigacion
Deposited on: 09 Feb 2015 17:05
Last Modified: 09 Feb 2015 17:05
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