Strategyproof Mechanisms for Additively Separable Hedonic Games and Fractional Hedonic Games

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.

💡 Research Summary

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The paper investigates strategy‑proof (truthful) mechanisms for two well‑studied classes of hedonic games: Additively Separable Hedonic Games (ASHGs) and Fractional Hedonic Games (FHGs). In these games each agent i assigns a numeric value v_i(j) to every other agent j. In ASHGs the utility of i in a coalition C_i is the sum of the values she assigns to the members of C_i, while in FHGs the same sum is divided by the size of the coalition, i.e., the utility is the average value. Agents are self‑interested and may misreport their valuations to improve their own utility. The authors adopt the mechanism‑design perspective without monetary transfers: a mechanism receives the reported valuations and outputs a partition of the agents into disjoint coalitions. A mechanism is strategy‑proof if no agent can increase her (expected) utility by lying, regardless of the reports of the others. The performance metric is the approximation ratio with respect to the utilitarian social welfare (the sum of all agents’ utilities).

Four natural families of valuation functions are considered:

1. General valuations: v_i(j) ∈