We describe Urban Driving Games (UDGs) as a particular class of differential games that model the interactions and incentives of the urban driving task. The drivers possess a “communal” interest, such as not colliding with each other, but are also self-interested in fulfilling traffic rules and personal objectives. Subject to their physical dynamics, the preference of the agents is expressed via a lexicographic relation that puts as first priority the shared objective of not colliding. Under mild assumptions, we show that communal UDGs have the structure of a lexicographic ordinal potential game which allows us to prove several interesting properties. Namely, socially efficient equilibria can be found by solving a single (lexicographic) optimal control problem and iterated best response schemes have desirable convergence guarantees.

中文翻译：

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具有词法偏好和社会效率纳什均衡的城市驾驶游戏

我们将城市驾驶游戏（UDG）描述为一类特殊的差分游戏，该模型对城市驾驶任务的相互作用和激励进行建模。驾驶员具有“共同的”兴趣，例如不互相碰撞，但在满足交通规则和个人目标方面也很感兴趣。受制于他们的身体动力学，代理人的偏好是通过词典关系表达的，该词典关系将不冲突的共同目标作为第一要务。在温和的假设下，我们表明，公共UDG具有以下结构：词典序序势博弈这使我们能够证明几个有趣的特性。即，可以通过解决单个（字典式）最优控制问题来找到有效的社会均衡，并且迭代的最佳响应方案具有理想的收敛性保证。