The study's central finding is that vehicle behavior in the analyzed trajectories did not fall neatly into one interaction pattern. Changes were frequently either concurrent - within 400 milliseconds of one another - or sequential, while one-sided events were much less common. Across the reported dataset and interaction cases, concurrent events accounted for 33.81% to 58.67% of cases, sequential events for 33.69% to 54.55%, and one-sided events for no more than 13.30%.
That mixture matters for models that represent how vehicles interact. The authors interpret the results as support for complementary game-theoretic descriptions: simultaneous-move formulations for changes that occur together, sequential formulations for ordered changes, and leader-follower formulations when ordering remains stable. The conclusion concerns timing visible in trajectories, not a direct account of vehicles' decision-making processes.
Turning trajectories into events
The researchers developed a trajectory-based framework to identify events in following, merging and conflicting interactions. Candidate pairs were found from road topology plus spatial and temporal compatibility, then grouped into candidate events. To verify a behavioral change, the analysis compared normalized speed deviations with vehicle-specific baselines. A pair was retained when at least one participant exceeded a normalized-deviation threshold of 2.0. For merging and conflicting candidates, the vehicles also had to encounter a shared region within 1.0 second.
The onset of a behavioral change was measured against a map-constrained reference trajectory. In plain terms, the observed speed had to depart from that reference by more than 0.3 metres per second continuously for at least 400 milliseconds. When both vehicles had detected onsets, the event was labeled concurrent if their onsets fell within a 400-millisecond tolerance; otherwise it was sequential. If only one onset was detected, it was one-sided, and if neither was detected, it was unresolved.
For the response analysis, each directed source-target pair treated one vehicle as the source and the other as the target. The target was checked for a new behavioral change after the source onset, using a post-onset search window of up to 2,000 milliseconds. Pairs were classified as response, preactive, no-response or right-censored. The response figures therefore describe assessable directed pairs under those rules.
The evaluation covered six trajectory datasets: INTERACTION, highD, inD, rounD, the Waymo Open Motion Dataset and nuPlan. The reported extracted-event counts were 765 for INTERACTION, 1,387 for highD, 225 for inD, 1,371 for rounD, 5,565 for Waymo and 2,566 for nuPlan.
Responses were common, but far from universal
Among assessable directed pairs, the chance of a detected response varied by dataset. It was 40.0% in INTERACTION, 42.8% in inD, 47.5% in rounD, 47.6% in highD, 27.1% in Waymo and 43.2% in nuPlan. Giving each dataset equal weight produced a mean of 41.4%, with a 95% confidence interval of 35.2% to 46.0%.
When responses were detected, about 64% occurred within the same 400-millisecond window used to classify concurrent changes. The share ranged from 56.4% to 69.5% across the six datasets. This result describes the timing of detected post-onset changes; it does not identify the internal processes behind them.
Sequential events also tended to keep the same order. Stable ordering - defined as fewer than two reversals in the sequence - accounted for 80.46% to 100.00% of sequential events across datasets and interaction types. Alternating ordering, defined as two or more reversals, was more visible in Waymo: it accounted for 19.54% of sequential following events, 19.39% of merging events and 17.17% of conflicting events.
To estimate uncertainty, the researchers used scene-level cluster bootstrap resampling with 2,000 replicates and percentile-based 95% confidence intervals. They also used a logistic mixed-effects model with a scene-level random intercept to examine heterogeneity, reporting adjusted odds ratios with 95% confidence intervals.
A map of timing, not a theory of minds
The paper's claim is deliberately narrower than its game-theory language might suggest. It measures observable behavioral-change timing, response patterns and ordering stability. It does not establish vehicles' decision-making processes, information sets, utility functions, strategies or equilibrium mechanisms. The proposed model choices are interpretations of the trajectory record, not direct observations of internal game processes.
That distinction is important when reading the response numbers. A response was counted only under a defined source onset, search window and classification scheme, so the result is about when changes appeared in the data and does not show that one change caused another. The study's broader message is that one interaction structure should not automatically be treated as universal; the observed mixture may call for different temporal assumptions in vehicle-interaction models.
The manuscript is an arXiv preprint dated 26 Aug 2026. It reports support from the National Natural Science Foundation of China under grants 62573289, 52402504 and U22A20100.
Paper data and sources
Original title: Choose Your Game Wisely: Measuring Game-Theoretic Structures in Real-World Vehicle Interactions
Authors: Yueyuan Li, Rongcheng Nie, Weijie Xi et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text