Selfish AV routing adds 1.7% to human drivers' commutes; a social cost term cuts it to 1.1%

Autonomous vehicle route choices impose an externality on human-driven vehicles: when autonomous vehicles minimize only their own travel time, human drivers' travel times rise relative to before those vehicles entered the system. Human drivers previously updated route utilities over repeated commutes until the system approached equilibrium; after autonomous vehicles entered and learned routing policies with multi-agent reinforcement learning, their selfish route choices changed that state. On the real Ingolstadt and Provins networks, human drivers' travel times lengthen at every examined autonomous-vehicle penetration rate; in Ingolstadt, selfish routing by 40% autonomous vehicles increases other vehicles' travel times by 1.7%.

Adding the social term to the autonomous-vehicle reward limits the rise in human drivers' travel times, and the autonomous vehicles' own average travel times are slightly shorter as well. Compared with selfish routing, the relative travel-time change for human drivers moves up once marginal cost is included, meaning their travel times are shorter than under selfish routing. In Ingolstadt that increase drops from 1.7% to 1.1%, and the effect is consistent across the tested cities, penetration rates, and replications.

Computing marginal cost only for the autonomous vehicles that most affect the system retains most of the benefit with fewer counterfactual simulations. Computing marginal cost for every autonomous vehicle requires one counterfactual simulation per vehicle per commute day; in Ingolstadt at 40% penetration, about 414 autonomous vehicles over 10,000 training iterations require about 4,140k counterfactual simulations. Computing marginal cost for the 40% most impactful autonomous vehicles cuts this to about 1,660k, and with the 800k joint-action samples used to identify impactful vehicles the total is about 2,456k, roughly a 40% reduction, while the human-driver relative travel-time change averages about 0.2 percentage points below the all-vehicle case.

The reward is validated on the real Ingolstadt and Provins networks across several autonomous-vehicle penetration rates and replications, with REINFORCE training and independent learners, though the reward form itself is not tied to that algorithm. In the experimental setting, departure times and demand stay constant across simulation days, the route set is fixed, human learning is disabled after autonomous vehicles are introduced, and human route choices are sampled from a fixed learned distribution. Selective marginal cost is evaluated on Ingolstadt at 40% penetration, with impactful vehicles identified from 800k joint-action samples.

As the weight on the social term grows, human drivers' travel times improve further, but autonomous-vehicle and overall system travel times worsen, and beyond a certain value both deteriorate. In Ingolstadt, raising the weight from 0 to 0.1 improves human-driver, autonomous-vehicle, and system travel times relative to before autonomous vehicles were introduced by 0.6, 0.1, and 0.4 percentage points respectively; raising it to 0.2 adds 0.1 percentage points for human drivers but reduces the relative travel-time change for autonomous vehicles and the system by 1.3 and 0.5 percentage points. Autonomous vehicles that receive the marginal-cost reward show smaller relative travel-time changes than selfish ones, so vehicles that account for their system impact may be individually worse off.