Location methods in experimental design

The design variables of an experiment is modelled as a facility location problem: we consider the case where the design variables are the coordinates of n points in a region of the plane and we look for the optimal configuration of the points under some constraints. In this paper we present a non-cooperative game theoretical model for the problem of experimental design: n virtual players decide the location of a point in the admissible region optimizing a pay-off function. The Nash equilibrium solutions will be the optimal solution of the design variables problem. The resulting game has nice properties, so that a computational procedure is performed by using genetic algorithm approach, together with some existence results