Geodesic
Bertrand--Nash equilibrium in the linear city model
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 10 (2018) no. 2, pp. 27-39

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The paper [1] explores the spatial duopoly of firms under Stackelberg competition, when one of the firms is the leader in terms of both volume of product and location. In this paper we consider the case of leadership only in terms of volume of product. Stackelberg–Nash equilibrium in the price and spatial strategies of firms are found. In the course of analysis of equilibrium stability, it is proved that the transport tariff is a bifurcation parameter for firms. It was found that the change in the central agglomeration strategy to the differentiation strategy occurs at the point of transcritical bifurcation. The conditions for full coverage of the markets for both strategies are defined. It is obtained that the Stackelberg information asymmetry leads to asymmetry of equilibrium locations of firms.
Keywords: linear city, agglomeration, differentiation, Stackelberg information asymmetry, transcritical bifurcation. 
@article{MGTA_2018_10_2_a1,
     author = {Serhij V. Melnikov},
     title = {Bertrand--Nash equilibrium in the linear city model},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {27--39},
     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2018_10_2_a1/}
}
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Serhij V. Melnikov. Bertrand--Nash equilibrium in the linear city model. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 10 (2018) no. 2, pp. 27-39. http://geodesic.mathdoc.fr/item/MGTA_2018_10_2_a1/