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

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Author(s): López M. Dolores | Rodrigo Javier | Sánchez José Manuel

Journal: American Journal of Operations Research
ISSN 2160-8830

Volume: 03;
Issue: 03;
Start page: 337;
Date: 2013;
Original page

Keywords: Game Theory | Approximated Equilibrium | Location | Computational Geometry | Convex Hull

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.
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