On the Stability and Fairness of Submodular Allocations

Panagiotis Kyriakis, Sérgio Pequito, Paul Bogdan

Abstract: We focus on the allocation of goods (or resources) among competitive agents under submodular utility functions. We introduce two quantities, namely stability and fairness, to characterize an allocation. Our definition of stability is motivated by the famous stable marriage problem and measures the incentive that the agents have to deviate from the allocation. Furthermore, we quantify the fairness using the maximin fairness ratio which stems from the maximin fair shares. These shares represent an ideal scenario wherein each agent is given the option to maximize her worst possible outcome. Following that, we design an efficient greedy round-robin algorithm for the submodular allocations problem. We prove that our algorithm gives a stable allocation and we extract a curvature-dependant maximin fairness ratio. To demonstrate the empirical performance of our algorithm, we conduct experimental studies and observe that the empirical fairness ratio is higher than 95% of the solution given by a brute-force approach, which outperforms the theoretical guarantee.