Key leaders in social networks

We then allow for an arbitrary sequence of players' moves. If we refine any sequence by making some groups of simultaneous movers act in sequence, their aggregate contribution increases. Consequently, the optimal sequence is a chain structure. When players have homogeneous intrinsic valuations, any chain, arbitrarily ordered, maximizes the aggregate contribution. We further consider the possibility of shrinking the number of stages needed for the optimal sequence. In general, our results hold when the network game exhibits strategic substitutes.