  We model the formation of networks as a game where players aspire to maximize
their own centrality by increasing the number of other players to which they
are path-wise connected, while simultaneously incurring a cost for each added
adjacent edge. We simulate the interactions between players using an algorithm
that factors in rational strategic behavior based on a common objective
function. The resulting networks exhibit pairwise stability, from which we
derive necessary stable conditions for specific graph topologies. We then
expand the model to simulate non-trivial games with large numbers of players.
We show that using conditions necessary for the stability of star topologies we
can induce the formation of hub players that positively impact the total
welfare of the network.
