On Maximizing Egalitarian Value in K-coalitional Hedonic Games

Abstract: This paper considers the problem of dividing agents among coalitions. We concentrate on Additively Separable Hedonic Games (ASHG's), in which each agent has a non-negative value for every other agent and her utility is the sum of the values she assigns to the members of her coalition. Unlike previous work, we analyze a model where exactly $k$ coalitions must be formed, and the goal is to maximize the utility of the agent which is worst off, i.e., the egalitarian social welfare. We show that this problem is hard, even when the number of agents should be equally divided among the coalitions. We thus propose a heuristic that maximizes the egalitarian social welfare and maximizes the average utility of each agent as a secondary goal. Using extensive simulations, both on synthetic and real data, we demonstrate the effectiveness of our approach. Specifically, our heuristic provides solutions that are much fairer than the solutions that maximize the average social welfare, while still providing a relatively high average social welfare.