TY - JOUR
AU - Kawase, Yasushi
AU - Sumita, Hanna
PY - 2020/04/03
Y2 - 2024/09/07
TI - On the Max-Min Fair Stochastic Allocation of Indivisible Goods
JF - Proceedings of the AAAI Conference on Artificial Intelligence
JA - AAAI
VL - 34
IS - 02
SE - AAAI Technical Track: Game Theory and Economic Paradigms
DO - 10.1609/aaai.v34i02.5580
UR - https://ojs.aaai.org/index.php/AAAI/article/view/5580
SP - 2070-2078
AB - <p>We study the problem of fairly allocating a set of indivisible goods to risk-neutral agents in a stochastic setting. We propose an (approximation) algorithm to find a stochastic allocation that maximizes the minimum utility among the agents. The algorithm runs by repeatedly finding an (approximate) allocation to maximize the total virtual utility of the agents. This implies that the problem is solvable in polynomial time when the utilities are gross-substitutes (which is a subclass of submodular). When the utilities are submodular, we can find a (1 − 1/<em>e</em>)-approximate solution for the problem and this is best possible unless P=NP. We also extend the problem where a stochastic allocation must satisfy the (ex ante) envy-freeness. Under this condition, we demonstrate that the problem is NP-hard even when every agent has an additive utility with a matroid constraint (which is a subclass of gross-substitutes). Furthermore, we propose a polynomial-time algorithm for the setting with a restriction that the matroid constraint is common to all agents.</p>
ER -