This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. I … existence result of D'Aspremont et al. (1979) does not extend to simple star graphs. I conjecture that this non-existence result …

that depends on the relative positions of the players within the graph. A collection of graphs will be called balanced if … lies in the core and the payoff vector is an element of payoff sets of all graphs in some balanced collection of graphs. We …