Empirically Calibrated Differential Games for Simulating Driver Interactions

Game-theoretic models provide principled frameworks for modeling vehicle interactions, but their underlying temporal assumptions have not been systematically examined against real-world driving behavior. In particular, it remains unclear how simultaneous, sequential, and asymmetric interaction structures can be measured from vehicle trajectories. This paper develops a trajectory-based interaction measurement framework to identify interaction events and quantify behavioral change onset, temporal organization, post-onset response dynamics, and ordering stability. The framework uses behavioral deviations to verify candidate interactions. We evaluate the framework on six real-world trajectory datasets, including INTERACTION, highD, inD, rounD, Waymo Open Motion, and nuPlan, covering diverse road geometries, traffic environments, and interaction types. The results show that concurrent and sequential behavioral changes both constitute substantial proportions of observed following, merging, and conflicting interactions. Among sequential interactions, stable ordering is more prevalent than alternating ordering, indicating that persistent asymmetric roles are a common interaction structure. Importantly, temporal precedence does not necessarily coincide with a measurable behavioral response, indicating that temporal ordering alone may not be sufficient to characterize behavioral dependence. These findings show that real-world interactions exhibit concurrent, sequential, and persistently ordered temporal structures. Different game-theoretic formulations are therefore better regarded as complementary modeling abstractions for different interaction regimes rather than as a universal structure governing all vehicle interactions.

Traffic microsimulators rely on hand-crafted behavior models that reproduce aggregate flow but miss the heterogeneous interactions between vehicles at signalized intersections. Learned trajectory predictors capture richer interactions but are short-horizon and tend to be unstable when run in closed loop. We present Enactor, an actor-centric generative model for closed-loop intersection microsimulation. The model focuses on vehicles; pedestrians are included as context that can influence vehicle decisions but not predicted. Dynamic actors and lane polylines are encoded in polar coordinates referenced to the intersection center. A transformer with separate spatial and temporal attention blocks predicts a distribution over each actor's next-step motion ($s$, $α$). Training uses a closed-loop curriculum so the model is exposed to its own predictions. We evaluate Enactor in two regimes. In a 4000-second simulation-in-the-loop test at two intersection geometries, Enactor controls every dynamic vehicle against a continuously refreshing actor set rather than the fixed cohort that learned trajectory predictors are usually evaluated against. It recovers the SUMO data generator's speed and travel-time distributions with KL divergence over an order of magnitude lower than a recent transformer baseline on travel time, and substantially lower on speed (roughly $5\times$ lower at Site 1), and reduces red-light violations relative to the same baseline by more than an order of magnitude. An ablation isolates the leader rear-bumper feature as the change with the largest effect on intersection-aware safety metrics. We also evaluate on real-world field data and apply the same architecture to naturalistic vehicle trajectories from a fish-eye camera at a signalized intersection and evaluate it on multi-horizon predictive tasks. Enactor outperforms a constant-velocity baseline at every horizon evaluated.

Traffic microsimulators are widely used to evaluate road network performance under various what-if" conditions. However, the behavior models controlling the actions of the actors are overly simplistic and fails to capture realistic actor-actor interactions. Deep learning-based methods have been applied to model vehicles and pedestrians as agents" responding to their surrounding environment" (including lanes, signals, and neighboring agents). Although effective in learning actor-actor interaction, these approaches fail to generate physically consistent trajectories over long time periods, and they do not explicitly address the complex dynamics that arise at traffic intersections which is a critical location in urban networks. Inspired by the World Model paradigm, we have developed an actor centric generative model using transformer-based architecture that is able to capture the actor-actor interaction, at the same time understanding the geometry to the traffic intersection to generate physically grounded trajectories that are based on learned behavior. Moreover, we test the model in a live simulation-in-the-loop" setting, where we generate the initial conditions of the actors using SUMO and then let the model control the dynamics of the actors. We let the simulation run for 40000 timesteps (4000 seconds), testing the performance of the model on long timerange and evaluating the trajectories on traffic engineering related metrics. Experimental results demonstrate that the proposed framework effectively captures complex actor-actor interactions and generates long-horizon, physically consistent trajectories, while requiring significantly fewer training samples than traditional agent-centric generative approaches. Our model is able to outperform the baseline in traffic related as well as aggregate metrics where our model beats the baseline by more than 10x on the KL-Divergence.