STABILITY OF NASH EQUILIBRIA IN LOCATIONAL GAMES

Consider a locational game on a network in which two competing facilit ies charge fixed, but not necessarily equal, prices and the decision v ariables are their respective locations. Rather than deciding in a giv en situation whether or not an equilibrium exists, we devise a stabili ty index that measures the stability or instability of a given situati on. In other words, given that an equilibrium exists, our index indica tes how much external effort (or subsidy) is required to destroy that equilibrium; if equilibria do not exist, the index shows how much exte rnal effort (or tax) is needed to ''generate'' an equilibrium. Computa tional evidence for randomly generated problems is presented.