A note on network games with strategic complements and the Katz-Bonacich centrality measure

We investigate a class of network games with strategic complements and bounded strategy sets by using the variational inequality approach. In the case where the Nash equilibrium of the game has some boundary components, we derive a formula which connects the equilibrium to the Katz-Bonacich centrality measure, thus generalizing the classical result for the interior solution case. Furthermore, we prove that any component of the Nash equilibrium is less than or equal to the corresponding component of the social optimal solution and numerically study the price of anarchy for a small size test problem.