A model of river pollution as a dynamic game with network externalities

Abstract

In network games, a network is an important attribute of players’ strategies: each player adopts her behavior not only by taking into account standard information about her opponents such as objectives, game dynamics, and information structure; but also by evaluating the communication structure of players represented by the network. In this paper, we investigate a dynamic game with network externalities in which a state variable of each player is influenced by her own decision and the decisions of her predecessors in the network. For the game under consideration, we identify Nash equilibrium and cooperative behavior. Additionally, we examine the model under myopic equilibrium and myopic cooperation where players place no weight on their future gains. Next, we use our findings to take in the important environmental problem of river pollution. We suppose that firms, which are located along the river flow, produce goods and compete in a market. The production results in water pollution, and the pollution emissions of a firm can influence downstream counterparts. We analyze this model in detail by incorporating a firm’s location and analytically comparing the equilibrium and cooperative behavior.