Equilibrium analysis of game on heterogeneous networks with coupled activities

We study a game where agents interacting over a network engage in two coupled activities and have to strategically decide their production for each of these activities. Agent interactions involve local and global network effects, as well as a coupling between activities. We consider the general case where the network effects are heterogeneous across activities, i.e., the underlying graph structures of the two activities differ and/or the parameters of the network effects are not equal. In particular, we apply this game in the context of palm oil tree cultivation and timber harvesting, where network structures are defined by spatial boundaries of concessions. We first derive a sufficient condition for the existence and uniqueness of a Nash equilibrium. This condition can be derived using the potential game property of our game or by employing variational inequality framework. We show that the equilibrium can be expressed as a linear combination of two Bonacich centrality vectors.