Selfish robotaxis shave their own commutes but add 1.7% to human drivers; a social cost term cuts that to 1.1%

Autonomous vehicles that pick routes to minimize their own travel time slow down human-driven vehicles sharing the same network, a cost that did not exist before they were introduced. Previously, human drivers converged toward a stochastic user equilibrium through repeated commuting, leaving the system near a stable state; after introduction, autonomous vehicles learn routing policies with multi-agent reinforcement learning whose objective contains only their own travel time. On the real networks of Ingolstadt and Provins, replacing 40% of vehicles with autonomous ones raises human-driven vehicles' average travel time by 1.7% over the pre-introduction level, and the direction holds across all tested penetration rates.

Writing marginal cost into the autonomous vehicle reward narrows the increase in human travel time, and the autonomous vehicles themselves do not get slower. Marginal cost is defined as the change in total travel time of all other vehicles when a given autonomous vehicle is removed from the simulation, measuring the extra time that vehicle imposes on the system. In Ingolstadt, adding the social term lowers the increase in human-driven vehicles' travel time from 1.7% to 1.1%; Provins shows the same narrowing, and autonomous vehicles' average travel time is slightly below that under purely selfish routing.

Computing marginal cost only for the most impactful autonomous vehicles reaches close to the full computation with fewer counterfactual simulations. The full version needs one counterfactual simulation per autonomous vehicle per day, about 4.14 million extra runs at 40% penetration in Ingolstadt over 10,000 training iterations. After ranking vehicles by a historical impact score, applying the marginal cost reward to only the 40% most impactful cuts extra simulations to about 1.66 million, or about 2.46 million including the 800,000 joint-action samples used to identify them, with human travel time about 0.2 percentage points below the full computation.

The findings rest on simulations of the two real networks of Ingolstadt and Provins, with demand, departure times and the set of available routes held constant across simulated days, and human route choices fixed to the learned distribution after autonomous vehicles are introduced. The intended readers are researchers and engineers working on traffic assignment, multi-agent reinforcement learning reward design, and urban network operations. The marginal cost reward form does not depend on a specific multi-agent algorithm; training used REINFORCE, and validation is limited to those two networks and the tested penetration rates.

The weight on the social term cannot grow without bound: beyond a certain value, human-driven vehicles keep improving while autonomous vehicles and overall system travel time get worse, with such a turning point in both Ingolstadt and Provins. At 10% most impactful vehicles, selective marginal cost leaves human travel time about 0.45 percentage points below the full computation, so too small a fraction loses effect. Among autonomous vehicles, those carrying the social term show a smaller relative travel-time change than those on the selfish reward, meaning the vehicles that account for system impact are not individually better off.