Local coordination and global congestion in random networks

This paper analyzes the impact of local and global interactions on individuals' action choices. Players are located in a network and interact with each other with perfect knowledge of their neighborhood and probabilistic knowledge of the complete network topology. Each player chooses an action, from some finite set, which imposes an externality on their neighbors as well as an externality on the complete network. Players deal with two opposing forces: they obtain utility from sharing their choices with their neighbors (positive local externality) but suiter disutility from sharing the same choice with all members of the network (negative global externality). Economic and social phenomena exhibiting these features are: the adoption of cost-reducing innovations, clusters of firms, time schedule choices, the adoption of subcultures and fads, among others. We find the conditions for the existence of all symmetric Bayesian Nash equilibria and translate them to a characterization in terms of the main properties of the network topol- ogy. The balance between local satisfaction and global dissatisfaction partially explains the equilibrium outcome. The players who finally decide on the type of equilibria are those that are either highly connected (hubs) or poorly connected (peripherals) to the others. On the one hand, hubs try to coordinate their action choices and on the other, peripherals are only worried about congestion and play the least selected actions of the network. Some examples illustrate our main results. As a by-product we also show the failure of symmetric