Price Competition on Graphs - Adriaan R. Soetevent (Tinbergen Institute, 2010)
This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. I propose an algorithm to calculate firm-level demand for anygiven graph, conditional on prices and firm locations. These graph models of price competitionmay lead to spatial discontinuities in firm-level demand. I show that the existence resultof D'Aspremont et al. (1979) does not extend to simple star graphs and I conjecture thatthis non-existence result holds more generally for all graph models with two or more firmsthat cannot be reduced to a line or circle.
Keywords: D43; L10; R12; 330; spatial competition; Hotelling; graphs; Hotelling-Modell; Preiswettbewerb; Nichtkooperatives Spiel; Graphentheorie