Spatial Cournot competition among multi-plant firms in a circular city

We characterize equilibrium plant locations for a spatial multi-plant Cournot oligopoly in a circular city. Previous work demonstrates that for a two-plant duopoly, all four plants are equally spaced. We establish that the equilibrium location pattern is unique if there are two firms with an equal number of plants. In most other scenarios, multiple equilibria arise. Next, we endogenously determine both the number of plants per firm and plant locations for a duopoly. It is shown that the subgame perfect Nash equilibrium may not be unique, and for identical set-up costs, the firms may choose different numbers of plants.