Efficient spatial competition

This paper uses the core to model the competition between the firms and shows that efficient location can be stable in situations with arbitrary distributions of buyers, arbitrary willingness-to-pay functions, and completely general location spaces.

Abstract

Game-theoretic models of spatial competition usually assume that firms set prices after their choices of locations. Rather than make this assumption, this paper uses the core to model the competition between the firms. Two conditions are shown to be sufficient for efficient spatial competition. The first is that the firms' location choices satisfy a no-externalities condition. The second is that the second-stage game satisfy a separable-value condition, namely that the value (gains from trade) can be created on a buyer-by-buyer basis. This approach yields two further benefits. First, efficient location can be stable in situations with arbitrary distributions of buyers, arbitrary willingness-to-pay functions, and completely general location spaces. Second, efficiency in location games can be shown to be related to the Second Welfare Theorem.