  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.
