  Game-theoretic motion planners are a powerful tool for the control of
interactive multi-agent robot systems. Indeed, contrary to predict-then-plan
paradigms, game-theoretic planners do not ignore the interactive nature of the
problem, and simultaneously predict the behaviour of other agents while
considering change in one's policy. This, however, comes at the expense of
computational complexity, especially as the number of agents considered grows.
In fact, planning with more than a handful of agents can quickly become
intractable, disqualifying game-theoretic planners as possible candidates for
large scale planning. In this paper, we propose a planning algorithm enabling
the use of game-theoretic planners in robot systems with a large number of
agents. Our planner is based on the reality of locality of information and thus
deploys local games with a selected subset of agents in a receding horizon
fashion to plan collision avoiding trajectories. We propose five different
principled schemes for selecting game participants and compare their collision
avoidance performance. We observe that the use of Control Barrier Functions for
priority ranking is a potent solution to the player selection problem for
motion planning.
