A Noncooperative Shipping Cournot Duopoly with Linear-Quadratic Transport Costs and Circular Space

The mixed strategy equilibria in a location quantity duopoly model with circular markets are investigated. We find that a continuum of equilibria exists when the transport cost function is linear. However, if costs are strictly concave or convex, most strategies fail to qualify as equilibria. For any integer n, there are nondegenerate mixed strategy equilibria in which each firm locates at n possible locations with equal probability. This result explains possible outcomes in which firms’ on-path locations are not minimally or maximally differentiated.