Abstract
This paper investigates the location game of two players in a spoke market with linear transportation cost. A spoke market model has been proposed, which is inspired by the Hotelling model and develops two-player games in price competition. Using two-stage (position and price) patterns and the backward guidance method, the existence of price and location equilibrium results for the position games is proved.
Highlights
In 1928, John von Neumann proved the basic principle of game theory [1]
Various position problems developed from the classical model were considered, and many results were obtained. e result of d’Aspremont et al [10] shows that the price equilibrium solution is ubiquitous for the modified Hotelling model and that the seller tends toward the difference of maximization. e Cournot competition with uneven distribution of consumers in a linear city model was studied in [11], and a necessary condition of agglomeration equilibrium was obtained. e author in [12] claimed that if there is no pure strategy equilibrium, the Hotelling model exhibits a mixedstrategy equilibrium. e Hotelling spatial competition model was extended by the author in [13] from three aspects: shape of the demand curve, the number of firms, and type of space
In the meantime, when the curvature of the utility functions is high enough, the existence of an equilibrium was proven. e relationship between the equilibrium location of the Hotelling model and the consumer density was analyzed by the authors in [15], and it was pointed out that the higher the consumer density, the closer the equilibrium position
Summary
In 1928, John von Neumann proved the basic principle of game theory [1]. Nowadays, game theory is a new field of modern mathematics and an important subject of operational research. e game theory mainly studies the interaction between the mathematical theory and the incentive structure for studying the competitive phenomena [2]. In [16], the author investigated the existence of equilibrium states in the Hotelling model in the case of n players and analyzed the effect of the number of companies on the equilibrium results of the Hotelling game. The results show that when the transportation cost is a linear function, there is a pure strategy price equilibrium.
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