Network formation games based on conditional independence graphs

The goal of this paper is to propose a network formation game where strategic agents decide whether to form or sever a link with other agents depending on the net balance between the benefit resulting from the additional information coming from the new link and the cost associated to establish the link. Differently from previous works, where the benefits are functions of the distances among the involved agents, in our work the benefit is a function of the mutual information that can be exchanged among the agents, conditioned to the information already available before setting up the link. An interesting result of our network formation game is that, under certain conditions, the final network topology tends to match the topology of the Markov graph describing the conditional independencies among the random variables observed in each node, at least when the cost of forming a link is small.