Stable group scheduling.

We consider the situation in which an organizer is trying to convene an event, and needs to decide on a schedule: a time slot and a set of invitees from a given set of agents. For each possible time slot, each agent has a single-peaked preference over the number of attendees at the event. Agent also has the outside option of not attending, which she prefers in some situations. The task of the organizer is to issue a maximum stable schedule -- the invited agents prefer attending to not attending, the agents not invited do not regret not being invited, and the event has the maximum number of attendees subject to these stability requirements. We consider both the non-strategic and strategic cases. In the former, in which agents truthfully reveal their preferences, we provide a polynomial-time algorithm for determining whether a stable schedule exists, and if it does, determining the maximum such schedule. In the strategic case we provide a truthful mechanism for the case in which the preferences of the agents are monotonically increasing, and an impossibility result for the general case.