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Game-theoretic motion planners are a powerful tool for the control ofinteractive multi-agent robot systems. Indeed, contrary to predict-then-planparadigms, game-theoretic planners do not ignore the interactive nature of theproblem, and simultaneously predict the behaviour of other agents whileconsidering change in one's policy. This, however, comes at the expense ofcomputational complexity, especially as the number of agents considered grows.In fact, planning with more than a handful of agents can quickly becomeintractable, disqualifying game-theoretic planners as possible candidates forlarge scale planning. In this paper, we propose a planning algorithm enablingthe use of game-theoretic planners in robot systems with a large number ofagents. Our planner is based on the reality of locality of information and thusdeploys local games with a selected subset of agents in a receding horizonfashion to plan collision avoiding trajectories. We propose five differentprincipled schemes for selecting game participants and compare their collisionavoidance performance. We observe that the use of Control Barrier Functions forpriority ranking is a potent solution to the player selection problem formotion planning.

Local Non-Cooperative Games with Principled Player Selection for Scalable Motion Planning