In interactive multi-agent settings, decision-making complexity arises from agents' interconnected objectives. Dynamic game theory offers a formal framework for analyzing such intricacies. Yet, solving dynamic games and determining Nash equilibria pose computational challenges due to the need of solving coupled optimal control problems. To address this, our key idea is to leverage potential games, which are games with a potential function that allows for the computation of Nash equilibria by optimizing the potential function. We argue that dynamic potential games, can effectively facilitate interactive decision-making in many multi-agent interactions. We will identify structures in realistic multi-agent interactive scenarios that can be transformed into weighted potential dynamic games. We will show that the open-loop Nash equilibria of the resulting weighted potential dynamic game can be obtained by solving a single optimal control problem. We will demonstrate the effectiveness of the proposed method through various simulation studies, showing close proximity to feedback Nash equilibria and significant improvements in solve time compared to state-of-the-art game solvers.

翻译：在交互式多智能体环境中，决策复杂性源于智能体之间相互关联的目标。动态博弈理论为分析此类复杂性提供了形式化框架。然而，由于需要求解耦合的最优控制问题，求解动态博弈并确定纳什均衡在计算上具有挑战性。为此，我们的核心思路是利用势博弈——这类博弈存在一个势函数，通过优化该函数即可计算纳什均衡。我们认为动态势博弈能够有效促进多智能体交互中的决策过程。我们将识别实际多智能体交互场景中可转化为加权势动态博弈的结构特性，并证明通过求解单一最优控制问题即可获得所得加权势动态博弈的开环纳什均衡。通过多项仿真研究，我们验证了所提方法的有效性：其结果与反馈纳什均衡高度接近，且求解时间相比现有最优博弈求解器有显著提升。