General distribution of consumers in pure Hotelling games

A pure Hotelling game is a competition between a finite number of players who select simultaneously a location in order to attract as many consumers as possible. In this paper, we study the case of a general distribution of consumers on a network generated by a metric graph. Because players do not compete on price, the continuum of consumers shop at the closest player's location. Under regularity hypothesis on the distribution we prove the existence of an epsilon-equilibrium in pure strategies and we construct it, provided that the number of players is larger than a lower bound.