A Formal Analysis of Required Cooperation in Multi-Agent Planning

It is well understood that, through cooperation, multiple agents can achieve tasks that are unachievable by a single agent. However, there are no formal characterizations of situations where cooperation is required to achieve a goal, thus warranting the application of multiple agents. In this paper, we provide such a formal characterization for multi-agent planning problems with sequential action execution. We first show that determining whether there is required cooperation (RC) is in general intractable even in this limited setting. As a result, we start our analysis with a subset of more restrictive problems where agents are homogeneous. For such problems, we identify two conditions that can cause RC. We establish that when none of these conditions hold, the problem is single-agent solvable; otherwise, we provide upper bounds on the minimum number of agents required. For the remaining problems with heterogeneous agents, we further divide them into two subsets. For one of the subsets, we propose the concept of transformer agent to reduce the number of agents to be considered which is used to improve planning performance. We implemented a planner using our theoretical results and compared it with one of the best IPC CoDMAP planners in the centralized track. Results show that our planner provides significantly improved performance on IPC CoDMAP domains.