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.

翻译：为了尽量减少多试剂路径规划问题中的碰撞风险,我们设计了一个配有多线性拥堵成本的马尔科夫决策流程拥堵游戏。游戏中的玩家完成个别任务,同时尽量减少自己的碰撞风险。我们显示,纳什平衡与非电流优化问题的第一级KKT点相吻合。我们的游戏适用于法国的历史飞行计划,以减少商用飞机的碰撞风险。