We in this paper investigate navigation strategies of two cross-moving connected and autonomous vehicles (CAVs) at an unsignalised intersection. As highly intelligent and automated entities, CAVs could make decisions independently or behave in a cooperative manner. A Nash game with discrete decision strategy is formulated to characterize the non-cooperative behaviour and a cooperative game is formulated to model the cooperative control mechanism. Results show that (i) pure-strategy Nash equilibria (NEs) for the non-cooperative game always exist and NEs hold if and only if at least one CAV takes its dominant strategy; (ii) more than two pure-strategy NE solutions may exist, but at most two different payoffs could arrive for each player at pure-strategy NEs; (iii) the optimal solution to the cooperative game must be in the NE solution set. These interesting findings provide useful managerial insights to CAV operators and transport authorities, and also enable us to tailor a branch & bound (B&B) algorithm to efficiently solve the models. We also extend the proposed methodology to the n-player case ($n\ge 3$) and give some more generalized insights. Numerical experiments are demonstrated in the end to test the computational accuracy and efficiency of the B&B method and show that our models and algorithm can be readily incorporated into future real-time CAV decision system to help navigate through unsignalised intersections.

我们在本文中研究了在无信号交叉口的两辆交叉移动的自动驾驶汽车 (CAV) 的导航策略。作为高度智能和自动化的实体，CAV 可以独立做出决策或以合作方式行动。制定了具有离散决策策略的纳什博弈来表征非合作行为，并制定合作博弈来对合作控制机制进行建模。结果表明（i）非合作博弈的纯策略纳什均衡（NEs）总是存在并且当且仅当至少一个 CAV 采取其优势策略时NEs成立；(ii) 可能存在两个以上的纯策略 NE 解决方案，但对于纯策略 NE 的每个参与者，最多可以达到两个不同的收益；(iii) 合作博弈的最优解必须在 NE 解集中。这些有趣的发现为 CAV 运营商和运输当局提供了有用的管理见解，并使我们能够定制分支定界 (B&B) 算法以有效地求解模型。我们还将拟议的方法扩展到n玩家案例（$n\ge 3$) 并给出一些更普遍的见解。最后通过数值实验来测试 B&B 方法的计算精度和效率，并表明我们的模型和算法可以很容易地融入未来的实时 CAV 决策系统，以帮助在无信号交叉口中导航。