A game theoretical model for experiment design optimization

Abstract

In this paper we present a noncooperative game theoretical model for the well known problem of experimental design. A virtual player decides the design variables of an experiment and all the players solve a Nash equilibrium problem by optimizing suitable payoff functions. The resulting game has nice properties, so that a computational procedure is performed by using genetic algorithm approach. 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. The problem arises from a concrete situation: find the optimal location of n receivers able to pick up particles of cosmic ray in a given platform (some experiment to measure the quantities of gamma rays are ongoing in Nepal thanks to the altitude of the region). Theoretical and computational results are presented for this location problem.