Algorithmic and game-theoretic approaches to group scheduling

Scheduling an event for a group of people is a notoriously frustrating task; it tends to be tedious, time consuming, and often leads to suboptimal schedules. One reason the problem has resisted a solution is that it has many dimensions, some of them easy to put one’s finger on, but others more subtle such as game-theoretic manipulability of the procedure. The first part of this work seeks algorithmic solutions to group scheduling problem. Assuming prompt and truthtelling agents, we can aim to design an efficient algorithm that finds the optimal scheduling process with respect to a given cost function. In Section 3 we formally define this as an optimization problem, and investigate the difficulty of the problem. We propose an efficient algorithm for finding the optimal solution, and then use the proposed algorithm in simulations to show that the result substantially outperforms the baseline approach in many realistic settings. The second part of this work puts more weight on the strategic behavior of agents. Imagine that agents have preferences over both the time and the number of attendees at the event. Given a set of invitees, the set is said to be stable if all invitees prefer attending to not attending, and if no uninvited person wishes she had been invited. Stability is obviously desirable, but in general a stable schedule may not exist; therefore it is interesting to know how hard it is to determine whether it exists (and to find the one that maximizes attendance). These questions take an extra meaning if agents can strategically misreport their preferences, and we answer these questions in Section 4.