Relationship Between Kronecker Graphs and Economic Theory...

As I am reading through material on Kronecker graphs I am thinking more deeply about the empirical properties of large graphs that that Kronecker graphs are able to capture, particularly the densification power law, and shrinking/stabilizing diameter.  It occurs to me that the densification property is actually implied by a number of micro-founded models of endogenous network formation.  In the economics literature, the key to achieving this densification process is for there to exist strategic complements in the link formation game (i.e., I want to form links if other people are also forming links).  In such games, the complete nework (which is as dense as a network can get) is typically an equilibrium network.  In sum, in the presence of strategic complements one should expect the network to become more dense over time.

In these economic network games with strategic complements it is generally assumed that agents have complete information on strategies, the number of other players, etc.  The ability to achieve complete network connectivity and thus maximum density depends on complete information.  However, in the real world, agents make link formation decision based on local information, and as such complete network connectivity and thus maximum density will not be very likely in practice (even if it were desirable in theory).  Here is an interesting question: is there a link between local information/asymmetric information and the power law densification process that shows up in the empirical data?  Do networks formed by self-interested agents acting on the basis of local information about link options densify according to a power law? A related question: how, if at all, are Kronecker graphs related to the behavior of sefl-interested agents?  To be continued...