Co-authorship model with link strength

We generalize a network formation model for co-authorship introducing the possibility of the connections having different link strengths. Different link strengths represent the fact that authors may put different efforts into different collaborations. To evaluate the model, we consider the notions of efficiency and pairwise stability, which are based on a utility function that measures the benefits for an author to belonging to a certain network structure. We divide the analysis in two cases, considering that link strengths are unbounded or bounded. In the first case, we show that if there are more than two authors in the network, then there is no pairwise stable network. In the second case, we show that the pairwise stable networks consist of completely connected disjoint components where essentially all link strengths are maximal. Regarding efficiency, in both cases, if the number of authors is even, then the unique efficient network structure consists of pairs of connected authors.