Strategic multi-layer network formation

We study the problem of strategic network formation among a set of nodes where each node forms links with other nodes in the network to maximize some utility. While previous work in this area has considered the formation of a single edge set between the nodes, we consider the problem of the strategic formation of multiple edge sets between the nodes, corresponding to different types of relationships. We start by considering the case where one edge set is chosen to minimize distances between nodes that are neighbors in another edge set. This corresponds to a generalization of distance-based utility functions studied in the literature. In this setting, we characterize efficient networks (that are optimal with respect to a global utility function), and pairwise stable networks (where individual nodes cannot benefit from the addition or removal of incident edges).We then generalize existing concepts of pairwise stability and improving paths for network formation to the multi-layer setting with arbitrary utility functions.