The competitive facility location game is a kind of competitive game in which service-providers select locations to place their facilities in order to maximize their profits.
Step 3 is simple: each consumer just selects the cheapest facility.
Suppose a producer P has its facility in location L. Then, the price it takes from consumer C must be at least Cost[C,L].
It is possible to prove that this is a potential game (The potential is the total social-welfare; when a new producer enters the game, the increase in social-welfare exactly equals the producer's profit).
The facility-location game may have other pure Nash equilibria, in which the social welfare is not maximal.
However, it is possible to prove that the social welfare in such equilibria is at least half the optimum.