Non-monotonic network effects and market entry

•Equilibrium firm entry may not be optimal in markets with product diversity.•With competition in price, entry is always excessive.•Entry remains excessive for goods with monotonic network effects.•Entry can be excessive or insufficient when network effects are non-monotonic.

The simple circular model of horizontal product differentiation, in which firms compete in price, is characterized by excessive firm entry in equilibrium. When non-monotonic network effects are present, this result no longer holds. If consumers differ in their optimal number of other consumers choosing their same good, entry in equilibrium can be insufficient.