Mechanisms for Fair Attribution

We propose a new framework for optimization under fairness constraints. The problems we consider model procurement where the goal is to optimize a buyer's utility while paying sellers in a manner that reflects their contribution to the buyer's utility. The payment rules we consider are natural interpretations of fairness based on concepts such as Shapley values and the nucleolus from cooperative game theory. The question in this setting is whether the outcome (measured in terms of the buyer's utility) produced by mechanisms that enforce fair payments is competitive with the outcome of a mechanism that simply pays agents their costs and is not committed to fair payments. Our main result shows that there exists a mechanism which guarantees a solution whose value is at least one third of the optimal unfair solution for any submodular utility function, and that this ratio is optimal. We discuss several special cases for which this approximation ratio can be improved and natural extensions.