The Covid-19 epidemic highlighted the significance of externalities: contacts with other people do not only affect our chances of getting infected but also our entire network.
We introduce a model for coalitional network stability in networks with widespread externalities. The network function form generalises the partition function form of cooperative games in allowing the network structure to be taken into account. The recursive core for network function form games generalises the recursive core for such environments and its properties also rhyme with the corresponding inclusion properties of the optimistic and pessimistic recursive cores and can be seen as a modification of pairwise stability to a coalitional setting where the involvement of more players allows for the — partial — internalisation of the externalities, but we also allow residual players to endogenously respond to any externalities that may affect them. We present two simple examples to illustrate positive and negative externalities. The first is of a favour network and show that the core is nonempty when players must pay transfers to intermediaries; this simple setting also models economic situations such as airline networks. The second models social contacts during an epidemic and finds social bubbles as the solution.