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It considers a network game with several tandem links, a single service provider, and some users with two kinds. To classify the networks into two systems, the service provider has to make corresponding price for each one. The first system's price is influenced by the second one. Applying the game theorem to analyze the problem, which is a Stackelberg game, the service provider sets the price and the non-cooperative users admit a unique Nash equilibrium point. When the Nash equilibrium point is positive, it discusses the range of price and the scale of proportion of the two kinds of users in the first system. It also gives the numerical example of the rates of the users' Nash equilibrium points and the revenue of the network to explain the significance of the proper price that the service provider should make.