Title: Strategyproof Mechanisms for Additively Separable Hedonic Games and Fractional Hedonic Games,
Abstract: Additively separable hedonic games and fractional hedonic games have received
considerable attention. They are coalition forming games of selfish agents
based on their mutual preferences. Most of the work in the literature
characterizes the existence and structure of stable outcomes (i.e., partitions
in coalitions), assuming that preferences are given. However, there is little
discussion on this assumption. In fact, agents receive different utilities if
they belong to different partitions, and thus it is natural for them to declare
their preferences strategically in order to maximize their benefit. In this
paper we consider strategyproof mechanisms for additively separable hedonic
games and fractional hedonic games, that is, partitioning methods without
payments such that utility maximizing agents have no incentive to lie about
their true preferences. We focus on social welfare maximization and provide
several lower and upper bounds on the performance achievable by strategyproof
mechanisms for general and specific additive functions. In most of the cases we
provide tight or asymptotically tight results. All our mechanisms are simple
and can be computed in polynomial time. Moreover, all the lower bounds are
unconditional, that is, they do not rely on any computational or complexity
assumptions.