Determining a Fair Border

Introduction. Suppose n countries border on a region the ownership of which is in dispute (Fig. 1). Is there a way of partitioning the disputed territory so each country receives a single piece adjacent to itself which it considers at least 1/n the total value of the territory, even though different parts of the territory may be valued differently by individual countries? The main purpose of this paper is to show that such fair borders always exist, under the quite natural assumption that each country's value of the territory is nonatomic (i.e., single points have value zero).