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.

在本文中，我们分析了间接网络效应和竞争对各自提供两种互补产品的两家公司的影响。我们首先用一般的网络效应来制定价格博弈，并证明它既不是超模博弈也不是亚模博弈。然后，我们导出具有线性需求函数的闭式Nash平衡。此外，我们检验了具有两个对称公司的模型，每个公司都有一个主要产品和一个次要产品，其中一个公司的主要产品是另一个公司的次要产品。我们发现，主要产品和次要产品的网络效应对均衡价格的影响不是对称的。而且，随着替代率的提高，当替代率较低且次要产品的网络效应与主要产品相比很弱时，公司可能会部分牺牲主要产品市场以促进次要产品市场。我们的数值分析表明，两个互补产品之间强大的外部性将使公司受益。最后，分析了具有对称产品结构和广义客户偏好的模型，以验证主要结果的鲁棒性。