# 14-131/VII (2014-10-02)

Pim Heijnen, University of Groningen; Adriaan Soetevent, University of Groningen
spatial competition, Hotelling, graphs
JEL codes:
D43, L10, R12

This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. We derive an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. These graph models of price competition may lead to spatial discontinuities in firm-level demand.
We show that the existence result of D'Aspremont et al. (1979) does not extend to simple star graphs and conjecture that this non-existence result holds more generally for all graph models with two or more firms that cannot be reduced to a line or circle.