Consider a two-stage non-cooperative Cournot game with location choice
involving n greater than or equal to 2 firms each with several facili
ties. There are m greater than or equal to 2 spatially separated marke
ts constituting the vertices of a network. Each firm first selects the
locations of their facilities and then selects the quantities to supp
ly to the markets to maximize its profit. There exists a Nash equilibr
ium in the quantities offered by each firm at the markets. Furthermore
, when the demand in each market is sufficiently large, each firm choo
ses to locate its facilities only at vertices. With linear demand in e
ach market, there exists a Nash location equilibrium.