This paper presents a game theoretic formulation of a graph traversal problem, with applications to robots moving through hazardous environments in the presence of an adversary, as in military and security scenarios. The blue team of robots moves in an environment modeled by a time-varying graph, attempting to reach some goal with minimum cost, while the red team controls how the graph changes to maximize the cost. The problem is formulated as a stochastic game, so that Nash equilibrium strategies can be computed numerically. Bounds are provided for the game value, with a guarantee that it solves the original problem. Numerical simulations demonstrate the results and the effectiveness of this method, particularly showing the benefit of mixing actions for both players, as well as beneficial coordinated behavior, where blue robots split up and/or synchronize to traverse risky edges.

翻译：本文针对图遍历问题提出了一种博弈论建模方法，应用于军事安防等场景中机器人需在对抗环境下穿越危险区域的问题。蓝方机器人团队在时变图建模的环境中移动，试图以最小代价抵达目标；红方则通过控制图结构变化来最大化该代价。该问题被构建为随机博弈模型，从而可通过数值方法计算纳什均衡策略。研究给出了博弈值的边界，并证明该解能确保解决原始问题。数值仿真验证了该方法的有效性，特别展示了双方参与者混合策略的优势，以及蓝方机器人通过分散与同步行动穿越风险边的协同行为效益。