We will demonstrate that multiple competitive agents can efficiently share a mobility infrastructure without the need for an external coordinator. Standard game-theoretic approaches to this problem fall short in case of dynamic systems as encountered in autonomous mobility, coordinated use of the mobility space, traffic congestion control, etc. We will develop a new mathematical formalism and computational methods blending the concept of game-theoretic and dynamic equilibria. Autonomous mobility is an important application due to the importance of fairness and efficiency in resource use, the large number of interacting agents, and the need for automated and scalable solutions.