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We model the formation of networks as a game where players aspire to maximizetheir own centrality by increasing the number of other players to which theyare path-wise connected, while simultaneously incurring a cost for each addedadjacent edge. We simulate the interactions between players using an algorithmthat factors in rational strategic behavior based on a common objectivefunction. The resulting networks exhibit pairwise stability, from which wederive necessary stable conditions for specific graph topologies. We thenexpand the model to simulate non-trivial games with large numbers of players.We show that using conditions necessary for the stability of star topologies wecan induce the formation of hub players that positively impact the totalwelfare of the network.

Game Theoretic Formation of a Centrality Based Network