Pricing strategies for competitive firms with indirect network effects

In this paper, we analyze the impact of indirect network effects and competition on two firms each offering two complementary products. We first formulate the pricing game with general network effects and show that it is neither a supermodular nor a submodular game. We then derive the closed-form Nash equilibrium with linear demand functions. Furthermore, we examine a model with two symmetric firms each having a major product and a minor product, where the major product of one firm is the minor one of the other. We find that the impacts of network effects of major and minor products on the equilibrium prices are not symmetric. Moreover, as the substitution rate increases, the firm might partially sacrifice the major product market to boost the minor product market when the substitution rate is low and the network effect of the minor product is quite weak compared to that of the major product. Our numerical analysis shows that strong externalities between the two complementary products will benefit the firms. Finally, the models with symmetric product structures and generalized customer preference are analyzed to verify the robustness of the main results.