Price competition on graphs

•This paper extends Hotelling’s model of price competition with quadratic costs to graphs.•Pure-strategy equilibrium existence is not sure for simple star graphs and given firm locations.•This non-existence result holds for all graphs that cannot be reduced to a line or circle.•Numerical examples cl...

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Bibliographic Details
Published in:Journal of economic behavior & organization 2018-02, Vol.146, p.161-179
Main Authors: Heijnen, Pim, Soetevent, Adriaan R.
Format: Article
Language:English
Subjects:
Graphs
Hotelling
Spatial competition
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Summary:•This paper extends Hotelling’s model of price competition with quadratic costs to graphs.•Pure-strategy equilibrium existence is not sure for simple star graphs and given firm locations.•This non-existence result holds for all graphs that cannot be reduced to a line or circle.•Numerical examples clarify for which graphs and firm location configurations equilibria exist. 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 graphs that cannot be reduced to a line or circle.
ISSN:0167-2681
1879-1751
DOI:10.1016/j.jebo.2017.12.011