Stability of nash equilibria in locational games

Consider a locational game on a network in which two competing facilities charge fixed, but not necessarily equal, prices and the decision variables are their respective locations. Rather than deciding in a given situation whether or not an equilibrium exists, we devise a stability index that measures the stability or instability of a given situation. In other words, given that an equilibrium exists, the present index indicates how much external effort (or subsidy) is required to destroy that equilibrium; if equilibria do not exist, the index shows how much external effort (or tax) is needed to ‘generate’ an equilibrium. Computational evidence for randomly generated problems is presented.