Manipulation of k-Coalitional Games on Social Networks

In many coalition formation games the utility of the agents depends on a social network. In such scenarios there might be a manipulative agent that would like to manipulate his connections in the social network in order to increase his utility. We study a model of coalition formation in which a central organizer, who needs to form $k$ coalitions, obtains information about the social network from the agents. The central organizer has her own objective: she might want to maximize the utilitarian social welfare, maximize the egalitarian social welfare, or simply guarantee that every agent will have at least one connection within her coalition. In this paper we study the susceptibility to manipulation of these objectives, given the abilities and information that the manipulator has. Specifically, we show that if the manipulator has very limited information, namely he is only familiar with his immediate neighbours in the network, then a manipulation is almost always impossible. Moreover, if the manipulator is only able to add connections to the social network, then a manipulation is still impossible for some objectives, even if the manipulator has full information on the structure of the network. On the other hand, if the manipulator is able to hide some of his connections, then all objectives are susceptible to manipulation, even if the manipulator has limited information, i.e., when he is familiar with his immediate neighbours and with their neighbours.