Monopolistic Duopoly

We delve into the Hotelling price competition game without assuming full market coverage, and derive three equilibrium configurations. Two of them are well-known: Hotelling duopoly, where firms set the prices with the aim of stealing customers from the rival, and the market is fully covered; Local Monopolies, where firms avoid strategic interaction and business stealing, and the market is partially covered. In the third, firms interact strategically to keep the market covered, while at the same time avoiding business stealing; we define it as Monopolistic Duopoly (MD) because it combines the characterizing features of the other two scenarios. Despite the existence of few contributions on MD, this equilibrium configuration has been substantially ignored. By spelling out the economics of MD and applying its intriguing properties to recent issues, we establish that MD has, instead, relevant implications for the Hotelling literature.