Today I read a paper titled “The Strategic Formation of Multi-Layer Networks”
The abstract is:
We study the strategic formation of multi-layer networks, where each layer represents a different type of relationship between the nodes in the network and is designed to maximize some utility that depends on the topology of that layer and those of the other layers
We start by generalizing distance-based network formation to the two-layer setting, where edges are constructed in one layer (with fixed cost per edge) to minimize distances between nodes that are neighbors in another layer
We show that designing an optimal network in this setting is NP-hard
Despite the underlying complexity of the problem, we characterize certain properties of the optimal networks
We then formulate a multi-layer network formation game where each layer corresponds to a player that is optimally choosing its edge set in response to the edge sets of the other players
We consider utility functions that view the different layers as strategic substitutes
By applying our results about optimal networks, we show that players with low edge costs drive players with high edge costs out of the game, and that hub-and-spoke networks that are commonly observed in transportation systems arise as Nash equilibria in this game.