  Models of spatial firm competition assume that customers are distributed in
space and transportation costs are associated with their purchases of products
from a small number of firms that are also placed at definite locations. It has
been long known that the competition equilibrium is not guaranteed to exist if
the most straightforward linear transportation costs are assumed. We show by
simulations and also analytically that if periodic boundary conditions in two
dimensions are assumed, the equilibrium exists for a pair of firms at any
distance. When a larger number of firms is considered, we find that their total
equilibrium profit is inversely proportional to the square root of the number
of firms. We end with a numerical investigation of the system's behavior for a
general transportation cost exponent.
