Efficient networks for a class of games with global spillovers

In this paper we examine efficient networks in network formation games with global spillovers that satisfy convexity and sub-modularity properties. Unlike the previous literature we impose these properties on individual payoff functions. We establish that efficient networks of this class of games are nested split graphs. This allows us to complete the work of Goyal and Joshi (2006) and Westbrock (2010) on collaborative oligopoly networks.