Location methods and nash equilibria for experimental design in astrophysics and aerospace engineering

In this chapter we present a survey of location methods based on Nash equilibria for the design of experiments. The solution of the location problem is given in the bi-dimensional case by means of a potential formulation and a Nash game. The most important definitions and proofs are reported. Two main application fields are employed to stress the capability of an ad hoc numerical methodology involved in the solution of the location problem. The first one refers to optimal (constrained) location of sensors collecting cosmic rays for astrophysics experiments. The second one concerns the design of experiment in aerospace engineering related to set of flight tests within the flight envelope of an airplane. An outlook on location-allocation problem in economics is considered for a linear city with congestion in the conclusions.