Discrete hotelling pure location games: potentials and equilibria

We study two-player one-dimensional discrete Hotelling pure location games assuming that demand f (d ) as a function of distance d is constant or strictly decreasing. We show that this game admits a best-response potential. This result holds in particular for f (d ) = w d with 0 ≤ 1. For this case special attention will be given to the structure of the equilibrium set and a conjecture about the increasingness of best-response correspondences will be made.