Game theoretic controller synthesis for multi-robot motion planning Part   I : Trajectory based algorithms
  We consider a class of multi-robot motion planning problems where each robot is associated with multiple objectives and decoupled task specifications. The problems are formulated as an open-loop non-cooperative differential game. A distributed anytime algorithm is proposed to compute a Nash equilibrium of the game. The following properties are proven: (i) the algorithm asymptotically converges to the set of Nash equilibrium; (ii) for scalar cost functionals, the price of stability equals one; (iii) for the worst case, the computational complexity and communication cost are linear in the robot number. 
Minghui Zhu, Michael Otte, Pratik Chaudhari, Emilio Frazzoli
cs.MA cs.GT cs.SY math.OC