Farsighted stable sets in Hotelling’s location games

We apply the farsighted stable set to two versions of Hotelling’s location games: one with a linear market and another with a circular market. It is shown that there always exists a farsighted stable set in both games, which consists of location profiles that yield equal payoff to all players. 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 in the literature that use some variant of Nash equilibrium. While this stable set is unique when the number of players is two, uniqueness no longer holds for both models when the number of players is at least three.

► Farsighted stable sets (FSSs) are applied to Hotelling’s location games.
► An FSS, consisting of location profiles yielding equal payoff to all players, exists.
► This FSS reflects both minimum differentiation and local monopoly.
► This FSS is unique when the number of players is two.
► The uniqueness no longer holds when the number of players is at least three.