Waiting in the queue on Hotelling’s Main Street

We consider a variant of Hotelling’s location model that was proposed by Kohlberg (1983): when choosing a firm, consumers take travel time and also (expected) waiting time, which again depends on the number of consumers choosing that firm, into consideration. If we assume that firms are symmetric, then we show that a subgame perfect equilibrium exists if there is an even, but small, number of firms and no subgame perfect equilibrium exists if there is an odd, but small, number of firms. Further, we illustrate by means of examples what other subgame perfect equilibria exist if we allow for asymmetric firms