Inequality in Congestion Games with Learning Agents

TL;DR

The paper studies inequality that arises when transport network expansions interact with heterogeneity in commuter learning, modeled via multi-agent Q-learning in congestion games. It introduces the dynamic Price of Learning ($PoL$) to quantify inefficiency during adaptation and analyzes a stylized Braess-like network with two sources and an Amsterdam metro abstraction. Results show that unequal learning rates amplify disparities and that expansions can raise efficiency while widening inequity, highlighting the need to consider learning dynamics in policy design. The findings motivate fairness-aware planning, such as targeted information, phased rollouts, and support for slower-to-learn groups to ensure equity accompanies efficiency gains.

Abstract

Who benefits from expanding transport networks? While designed to improve mobility, such interventions can also create inequality. In this paper, we show that disparities arise not only from the structure of the network itself but also from differences in how commuters adapt to it. We model commuters as reinforcement learning agents who adapt their travel choices at different learning rates, reflecting unequal access to resources and information. To capture potential efficiency-fairness tradeoffs, we introduce the Price of Learning (PoL), a measure of inefficiency during learning. We analyze both a stylized network -- inspired in the well-known Braess's paradox, yet with two-source nodes -- and an abstraction of a real-world metro system (Amsterdam). Our simulations show that network expansions can simultaneously increase efficiency and amplify inequality, especially when faster learners disproportionately benefit from new routes before others adapt. These results highlight that transport policies must account not only for equilibrium outcomes but also for the heterogeneous ways commuters adapt, since both shape the balance between efficiency and fairness.

Figures (6)

• Figure 1: A Braess's Paradox game with two sources ($S1$ & $S2$) connecting to a single destination node $B$. We examine two phases: before and after the network extension $I_{CD}$ (red link).
• Figure 2: Top: The Amsterdam Metro Environment with key stations and routes for two commuter sources (West and East) converging at Central (See the Appendix for an overlay on the actual Metro Network Map). Three network phases are shown: Phase A (pre-2018, no North–South line), Phase B (current, with North–South line), and Phase C (future expansion connecting West and East via Amstel). Edge labels indicate free-flow travel times. Bottom: Arrow sizes indicate flows under the Nash Equilibrium, illustrating route choices and congestion distribution.
• Figure 3: Top: With equal learning rates, the system converges to a profile between the Social Optimum and the Nash Equilibrium. Source disparity fluctuates around zero, indicating fairness across sources. Bottom: With unequal rates, agents with higher learning rates gain a persistent advantage. The system converges to inequitable states even though the price of learning is comparable.
• Figure 4: When varying the relative learning rates between the two sources, disparities emerge after the intervention: agents with slower learning rate experience worse travel times than the faster-learning ones. This effect is most pronounced when learning rates differ sharply (e.g., 5:1 or 1:5).
• Figure 5: Training under uniform learning rates in the Amsterdam Metro network. We show the evolution of social cost and source disparity over training, for Phases A, B, and C. While the system eventually converges to the Nash Eq., learning inefficiencies and oscillations in source disparity highlight the unequal effects of adaptation even under homogeneous learning.