The Average-Value Allocation Problem
Abstract
We initiate the study of centralized algorithms for welfare-maximizing allocation of goods to buyers subject to average-value constraints. We show that this problem is NP-hard to approximate beyond a factor of e/(e-1), and provide a 4e/(e-1)-approximate offline algorithm. For the online setting, we show that no non-trivial approximations are achievable under adversarial arrivals. Under i.i.d. arrivals, we present a polytime online algorithm that provides a constant approximation of the optimal (computationally-unbounded) online algorithm. In contrast, we show that no constant approximation of the ex-post optimum is achievable by an online algorithm.
