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