A Formal Analysis of Required Cooperation in Multi-agent Planning

Research on multi-agent planning has been popular in recent years. While previous research has been motivated by the understanding that, through cooperation, multi-agent systems can achieve tasks that are unachievable by single-agent systems, there are no formal characterizations of situations where cooperation is required to achieve a goal, thus warranting the application of multi-agent systems. In this paper, we provide such a formal discussion from the planning aspect. We first show that determining whether there is required cooperation (RC) is intractable is general. Then, by dividing the problems that require cooperation (referred to as RC problems) into two classes -- problems with heterogeneous and homogeneous agents, we aim to identify all the conditions that can cause RC in these two classes. We establish that when none of these identified conditions hold, the problem is single-agent solvable. Furthermore, with a few assumptions, we provide an upper bound on the minimum number of agents required for RC problems with homogeneous agents. This study not only provides new insights into multi-agent planning, but also has many applications. For example, in human-robot teaming, when a robot cannot achieve a task, it may be due to RC. In such cases, the human teammate should be informed and, consequently, coordinate with other available robots for a solution.