Distance Hedonic Games

Michele Flammini, Bojana Kodric, Martin Olsen, Giovanna Varricchio

Abstract: In this paper we consider Distance Hedonic Games, a class of non-transferable utility coalition formation games that properly generalizes previously existing models, like Social Distance Games and Fractional Hedonic Games. In particular, in Distance Hedonic Games we assume the existence of a scoring vector α, in which the i-th coefficient αi expresses the extent to which x contributes to the utility of y if they are at distance i. We focus on Nash stable outcomes and consider two natural scenarios for the scoring vector: monotonically decreasing and monotonically increasing coefficients. In both cases we give NP-hardness and inapproximability results for the problems of finding a social optimum and a best Nash stable outcome. Moreover, we characterize the topologies of coalitions with high social welfare and give bounds on the Price of Anarchy and on the Price of Stability.