Duopoly pricing game in networks with local coordination effects

In this paper, we study a duopoly pricing problem in which two firms compete for selling two products in a network. Our proposed model consists of two stages. In the first stage, firms set the price they charge agents for their product and the quality of the product they offer. For agents, the quality of the product can be interpreted as the payoff of a local coordination game played among them in the network. In the second stage, agents in the network decide what fraction of these two products to purchase. We first characterize the Nash equilibrium of the game played among agents in the network. We show that agents' actions in the Nash equilibrium consist of two terms, one of which is proportional to the agents' centrality in the network. Conditioned on agents playing the equilibrium policy, we find the Nash equilibrium of the pricing game played between firms. We show that even when firms are similar and offer a uniform price for agents, their Nash equilibrium price depends on the network structure.We then analyze sensitivity of the agents' consumption with respect to the price and quality of the product. We finally show that depending on a firm's opponent's price and quality, the optimal price of a firm can be higher, equal or less than the monopoly optimal price.