Maximizing Social Welfare Subject to Network Externalities: A Unifying Submodular Optimization Approach

We consider the problem of maximizing social welfare by allocating indivisible items to a set of agents subject to network externalities. We first provide a general formulation that captures some of the known models as a special case. We then show that the social welfare maximization problem benefits some nice sub-or supermodular properties. That allows us to devise simple polynomial-time approximation algorithms using Lov\'asz extension and multilinear extension of the objective function. Our principled approach recovers or improves some of the existing algorithms and provides a simple unifying method for maximizing social welfare subject to network externalities.