A Locating Model With Network Externality

Game theory is the study of the ways in which strategic interactions among rational players produce outcomes with respect to the preferences (or utilities) of those players, none of which might have been intended by any of them. With the development of several decades, Game theory has made astonishing achievements at almost each related aspect; especially, game theory has been playing an even more important role on Economics. Hotelling Model was given by Harold Hotelling in 1929. using linear Model to study Spatial Competition between merchants at first. Suppose both companies have no marginal production cost, under principle of profit max-imization, each company wants to locate his shop at the middle of the city, i.e Principle of Minimum Differentiation. In 1979, with the same idea, D.Aspremont, Gabszewicz and Thisse made some amendment to its as-sumption, but they got a completely different, result. Under Bertrand Com-petition, the center locating of companies will make the equilibrium price zero; as a result, they will locate at the ends of the linear city, i.e Principle of Maximum Differentiation. It brought an extensive discussion on whether Principle of Maximum Differentiation holds or Principle of Minimum Dif-ferentiation holds. Since location differentiation of companies in a linear city can be derived as differentiation of products, Hotelling Model also can be used to decide what kind of competition strategy to adopt, compatable marketing or differentiated marketing.In this paper, we analyze the network externality company's locating and pricing strategy in Hotelling model which has a Stackelberg game in a class of uncertain information assumption. And we draw some relevant conclusions which include the following aspects:1. Introduce the network externality and a special uncertain informa-tion assumption in the extended Hotelling model which has a two-stage Staekelberg game, use a inverse regression method. and finally find the company's pricing strategy and the expected profits.2. Analyze the company's first-stage locating strategy under a special assumption and find the tendency of the company's locating strategy in different assumptions:Ⅰ. Under given f, when g∈S1 (S2), both companies' profits are monotonically increasing (decreasing) functions of g, which means the companies prefer to locate at the " high (low) " position in the linear city.Ⅱ. Under given g, when f∈S3 (S4), both companies' profits are monotonically increasing (decreasing) functions of f, which means the companies prefer to locate at the " ends (center) " of the linear city, viz.: the maximum (minimum) of differentiation.