1. IntroductionSince the seminal work of Hotelling (1929), a rich and diverse literature on spatial competition has emerged. Location models can be classified into two types. One type is shipping or spatial price-discrimination model, where sellers bear transport costs. The other is shopping or mill-pricing model, where buyers pay for transport. For each type, one can have either Bertrand-type price setting or Cournot-type quantity setting.1Most studies on location theory use shopping (mill pricing) models with Bertrand competition. Although Cournot and Bertrand-types of non spatial models are equally popular, the body of literature on spatial competition that uses Cournot-type models is relatively small. Economists have recently considered shipping models with Cournot competition. Hamilton, Thisse, and Weskamp (1989) and Anderson and Neven (1991) carry out pioneering works on location models.2 They use linear city models and show that all firms agglomerate at the central point. Pal (1998) shows that their result is crucially dependent on the assumption of a linear city. He investigates a circular city duopoly model3 and finds that an equidistant location pattern appears in equilibrium; that is, locational dispersion appears.4 Matsushima (2001a) extends Pal's model to an n-firm oligopoly and shows another equilibrium where half of the firms locate at one point and the other half locate at the opposite point (partial agglomeration). These results indicate the multiplicity of equilibria in spatial Cournot models with a circular city. The multiplicity of equilibria restricts the applicability of the model because the model does not give us a distinct prediction. In this article, we take a close look at Pal (1998) and Matsushima (2001a). We try to solve this problem by extending their linear transport cost model to one with nonlinear transport cost.5 We consider a simplified model. The numbers of firms and markets (and so possible locations) are four. Four firms choose location A, B, C, or D (see ). If each of the four firms chooses a different location, we call this outcome Pal type. If two firms locate at A and the other two locate at C, we call this outcome Matsushima type. We find that the Pal-type equilibrium is much more robust because (i) Pal-type equilibrium always exists as long as transport cost is increasing in distance, while Matsushima-type equilibrium fails to exist when the transport cost function is significantly convex or concave (Proposition 1); (ii) if firms choose their locations sequentially, the unique equilibrium outcome is Pal type under nonlinear transport cost functions (Proposition 2); and (iii) the profit of each firm in Pal type is never smaller than that in Matsushima type, and the former is strictly larger if the transport cost function is nonlinear (Proposition 3).We also compare the welfare implications of Pal-type and Matsushima-type models. If the transport cost function is linear, the two outcomes yield exactly the same profits, consumer surplus, and total social surplus. However, this equivalence does not hold if the transport cost function is nonlinear, either convex or concave. In this case, Pal type yields greater total social surplus and profit of each firm, while Matsushima type yields greater consumer surplus. These results indicate that the welfare implications are sensitive to whether or not the transport cost function is linear.Anderson and Neven (1991) show that, in the linear city model, a strong concavity in transport cost changes the equilibrium outcome. This result is related to our results, but we emphasize that our results are different from theirs. First, we show that both concavity and convexity of the transport cost function affect the results, while in Anderson and Neven (1991), only strong convexity changes the result. Second, in our Propositions 2 and 3, even a slight nonlinearity changes the results. …