  To minimize collision risks in the multi-agent path planning problem with
stochastic transition dynamics, we formulate a Markov decision process
congestion game with a multi-linear congestion cost. Players within the game
complete individual tasks while minimizing their own collision risks. We show
that the set of Nash equilibria coincides with the first-order KKT points of a
non-convex optimization problem. Our game is applied to a historical flight
plan over France to reduce collision risks between commercial aircraft.
