On Nash equilibria of a competitive location problem

The location-quality decision of a facility for two competing suppliers in a new market is described by a Huff-like attraction model where the profit that can be reached by each supplier depends on the actions of its competitor. We study the profit maximization problem of the suppliers under binary and proportional customer choice rules, assuming that they make their decisions simultaneously. The main questions are: what are the possible Nash equilibria in such a situation, how are they characterised and by which computational methods can they be determined? We report on finding