Spatial Cournot equilibrium: do branches matter?
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This paper aims to contribute to the literature of Cournot spatial equilibria in two-dimensional spaces by considering branching. We study the case in which two firms compete on a circle and each one has the possibility of opening one or more branches. An innovative method—polar coordinates—is employed to obtain the complex profit functions. We show that there exists a symmetric subgame perfect Nash equilibrium where both firms place their n branches alternately and at the same distance from the center of the circle. Additionally, we show that this is, up to rotation, the unique symmetric equilibrium location.
JEL ClassificationD43 L13
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