Farsighted stable sets in hotelling's location games

We apply farsighted stable set to two versions of Hotelling's location games: one with linear market and another with circular market. It is shown that there always exists a farsighted stable set in both games. In particular, the set of all location profiles that yields equal payoff across all players is shown to be a farsighted stable set. This stable set contains location profiles that reflect minimum differentiation as well as those profiles that reflect local monopoly. These results are in contrast to those obtained by equilibrium analysis. While the stable set uniquely exists when the number of players is 2, the uniqueness is not guaranteed when n>=2. In particular, we exhibit multiple stable sets in three person location games. We provide possible interpretations of these farsighted stable sets from the viewpoint of players' bargaining power and coalition.