  We consider the situation in which an organizer is trying to convene an
event, and needs to choose a subset of agents to be invited. Agents have
preferences over how many attendees should be at the event and possibly also
who the attendees should be. This induces a stability requirement: All invited
agents should prefer attending to not attending, and all the other agents
should not regret being not invited. The organizer's objective is to find the
invitation of maximum size subject to the stability requirement. We investigate
the computational complexity of finding the maximum stable invitation when all
agents are truthful, as well as the mechanism design problem when agents may
strategically misreport their preferences.
