  We consider the problem of allocating multiple indivisible items to a set of
networked agents to maximize the social welfare subject to network
externalities. Here, the social welfare is given by the sum of agents'
utilities and externalities capture the effect that one user of an item has on
the item's value to others. We first provide a general formulation that
captures some of the existing models as a special case. We then show that the
social welfare maximization problem benefits some nice diminishing or
increasing marginal return properties. That allows us to devise polynomial-time
approximation algorithms using the Lovasz extension and multilinear extension
of the objective functions. Our principled approach recovers or improves some
of the existing algorithms and provides a simple and unifying framework for
maximizing social welfare subject to network externalities.
