Dipartimento di Ingegneria informatica, automatica e gestionale

The problem of inconsistent planning in decision making, which leads to undesirable effects such as procrastination, has been studied in the behavioral-economics literature, and more recently in the context of computational behavioral models. Individuals, however, do not function in isolation, and successful projects most often rely on team work. Team performance does not depend only on the skills of the individual team members, but also on other collective factors, such as team spirit and cohesion. It is not an uncommon situation (for instance, experienced by the authors while working on this paper) that a hard-working individual has the capacity to give a good example to her team-mates and motivate them to work harder. In this paper we adopt the model of Kleinberg and Oren (EC'14) on time-inconsistent planning, and extend it to account for the influence of procrastination within the members of a team. Our first contribution is to model collaborative work so that the relative progress of the team members, with respect to their respective subtasks, motivates (or discourages) them to work harder. We compare the total cost of completing a team project when the team members communicate with each other about their progress, with the corresponding cost when they work in isolation. Our main result is a tight bound on the ratio of these two costs, under mild assumptions. We also show that communication can either increase or decrease the total cost. We also consider the problem of assigning subtasks to team members, with the objective of minimizing the negative effects of collaborative procrastination. We show that whereas a simple problem of forming teams of two members can be solved in polynomial time, the problem of assigning n tasks to n agents is NP-hard.