Abstract:
We study spatial competition by firms which is often studied in the context of linear markets where customers always shop at the nearest firm. Here, customer behavior is determined by a probability vector p=(p1,...,pn) where pi is the probability that a customer visits the ith closest firm. At the same time, the market is circular a là Salop (Bell J Econ 10(1):141–156, 1979), which has the advantage of isolating the impact of customer shopping behavior from market boundary effects. We show that non-convergent Nash equilibria, in which firms cluster at distinct positions on the market, always exist for convex probability vectors as well as probability vectors exhibiting a certain symmetry. For concave probability vectors, on the other hand, we show that non-convergent Nash equilibria are unlikely to exist.