Truthful Mechanisms for Proportionally Fair Allocations

We study the problem of designing mechanisms to allocate a heterogeneous set of divisible goods among a set of agents in a fair manner. We consider the well known solution concept of proportional fairness that has found applications in many real-world scenarios. Although finding a proportionally fair solution is computationally tractable, it cannot be implemented in a truthful manner. To overcome this, in this paper, we give mechanisms which are truthful and achieve proportional fairness in an approximate manner. We use a strong notion of approximation, requiring the mechanism to give each agent a good approximation of its proportionally fair utility. A motivating example is provided by the massive privatization auction in the Czech republic in the early 90s.