Group Activity Selection Problem

We consider a setting where we have to organize one or several group activities for a group of agents. Each agent will participate in at most one activity; her preference over activities generally depends on the number of participants in the activity. The goal is to assign agents to activities in a desirable way. We give a general model, which is a natural generalization of anonymous hedonic games (and can also be expressed, in a less natural way, as a hedonic game). Two well-known solution concepts in hedonic games, namely individual rationality and Nash stability, are particularly meaningful for our model. We study, from the computational point of view, some existence and optimization problems related to these two solution concepts, in the general case as well as for natural restrictions on the agents’ preferences.