Some stackelberg type location game

This paper considers a Stackelberg type location game over the unit square [0,1] × [0,1]. There are two chain stores, Players I and II, which sell the same kind of articles. Each store is planning to open a branch in region [0,1]. The purpose of each store is to decide the location to open its branch. In such a situation, the demand points, i.e., the customers, distribute continuously over [0,1] in accordance with cdf G(•). Each customer wants to buy at a closer store between them, but never moves more than a distance ℓ. We also assume that Player I is forced to behave as the leader of this game and the opponent (Player II) is to be the follower. It is shown that there are various types of Stackelberg equilibriums according to the conditions of G(•) and ℓ.