Agent-Based Evolutionary Dynamics for Mixed Autonomy Weaving Ramps

1. INTRODUCTION

• Freeway weaving remains a persistent bottleneck, and CAV lane choices offer a way to influence traffic while remaining decentralized.Prior macroscopic work incorporates social value orientation into CAV objectives and characterizes when altruistic CAVs improve traffic efficiency [4] [18].Source: §1 · p. 1
• The macroscopic model leaves open whether decentralized finite fleets can reach its equilibrium and how adaptation, heterogeneous altruism, and imperfect information affect outcomes.Existing vehicle-level models also do not reproduce the calibrated cost structure and penetration thresholds of the weaving-ramp model.Source: §1 · p. 1
• The paper treats the calibrated macroscopic model as a specification, inheriting its equilibrium costs and penetration benchmarks while adding vehicle-level dynamics and deployment studies.The vehicle-level dynamics and convergence analysis are novel contributions.Source: §1 · pp. 1–2
• Replicator-based adaptation yields an exact potential game whose dynamics converge globally to the unique Wardrop equilibrium.The agent-based framework also examines convergence regimes, demand tracking, distributional outcomes, heterogeneous altruism, imperfect observability, and belief sharing.Source: §1 · p. 2

2.1 Population-game Model

• Replicator dynamics increase the share of lower-cost strategies, and their interior stationary points coincide with Wardrop equilibria.The discrete-time agent-based update converges to the replicator ODE as population size grows and step size shrinks; an exact potential can establish stability.Source: §2.1 · p. 2
• SVO uses an altruism angle to weight private cost against marginal social cost, from fully selfish at θ = 0 to fully altruistic at θ = π/2.The sine–cosine weights parameterize those concerns.Source: §2.1 · p. 2

2.2 Weaving Ramp Model

• The model represents a two-lane weaving section where through vehicles choose to stay or bypass, with lane costs calibrated to demand and traffic composition.The setup distinguishes entering, exiting, and through movements and abstracts within-section spatial dynamics into lane-cost functions.Source: §2.2 · p. 2
• Altruistic CAVs interpolate the mixed-population equilibrium between the HDV Wardrop point and social optimum; aggregate social cost stays at baseline, falls, then saturates as penetration rises.The three phases are unchanged cost at low penetration, strict decrease at intermediate penetration, and social-optimum saturation at high penetration.Source: §2.2 · p. 3

Agents and Lane-Choice Dynamics

• Vehicles update their steadfast-lane probabilities with a decentralized replicator rule using their own altruism angle, realized lane costs, and demand composition.The operator’s intervention is choosing the altruism angle broadcast to CAVs.Source: §3 · p. 3

Mean-Field Approximation and Convergence

• The scalar mean-field approximation models aggregate change as x(1−x) times the population-average incentive, assuming individual probabilities remain concentrated around their average.Time is rescaled as τ = ηt.Source: §3 · p. 3
• Under the homogenization closure and stated positivity conditions, the aggregate potential has a unique maximizer that is the unique interior Wardrop equilibrium and is globally asymptotically stable.The interior maximizer is also the unique symmetric Nash equilibrium and is evolutionarily stable under u = −J.Source: §3 · pp. 3–4

Heterogeneous Fleets

• With heterogeneous CAV altruism, expected aggregate dynamics match a homogeneous model with effective angle and penetration, but finite fleets may differ through type-correlated choices and sampling variability.Altruism heterogeneity reduces effective aggregate influence unless all CAVs share the same angle.Source: §3 · p. 4

Partial Observability and Cooperative Belief Sharing

• Vehicles may use only their latest local observation or fuse independent observations through shared beliefs, whose Bayesian update yields a posterior-mean demand estimate.The memoryless estimator uses the most recent observation; belief sharing combines information received from vehicles or roadside infrastructure.Source: §3 · p. 4
• For either demand estimator, the expected replicator field and equilibrium location match full information; variance is O(σ²_obs) for memoryless estimates and decays as 1/t under belief sharing.The effective-cost difference is affine in demand, so unbiased estimates preserve its expected value.Source: §3 · p. 4

Macroscopic-equilibrium validation

• The HDV-only ABM, closed-form Wardrop equilibrium, and independent SUMO simulation agree within 1–2% across tested demand conditions.This validates the ABM steady-state bypass fraction against both an analytic benchmark and an independent simulation.Source: §4 · p. 4, Figure 1 · p. 5
• The mixed-traffic ABM and analytic equilibrium recover an HDV baseline for p ≤ p1, a decreasing transition, and a θ-dependent floor for p ≥ p2.The comparison spans CAV penetration p and altruism angle θ.Source: §4 · p. 4, Figure 2 · p. 5

Heterogeneous fleets

• Fleet profiles with the same effective altruism angle produce nearly identical equilibria, while greater heterogeneity primarily affects transient convergence.All tested homogeneous and mixed profiles retain the three-regime structure.Source: §4 · p. 5, Figure 3 · p. 5

Convergence speed and stability

• At θ = π/2, low-penetration fleets require conservative learning rates, whereas higher penetration supports faster adaptation without sustained oscillation.Fig. 4 reports settling time over CAV penetration p and learning rate ηCAV.Source: §4 · p. 5, Figure 4 · p. 5

Tracking time-varying demand

• Demand-tracking RMSE is ≈0.007 for period 200 and 0.012 for period 40, with more accurate tracking under slowly varying demand.The ABM trajectory is compared with the instantaneous quasi-static equilibrium.Source: §4 · p. 5, Figure 5 · p. 5

Distributional outcomes and free-riding

• The fully altruistic fleet has the highest measured inequity (G ≈0.014), while mixed profiles have lower inequity (G ≈0.009).The results indicate that full altruism can concentrate conflict-zone delay on vehicles absorbing that delay.Source: §4 · p. 5, Figure 6 · p. 5

Partial observability and belief sharing

• Observation noise delays transitions between penetration regimes but does not change the social-optimum floor, and cooperative belief sharing is closer to perfect information than memoryless estimation.Fig. 7 compares social cost across the three information settings.Source: §4 · pp. 5–6, Figure 7 · p. 6

Recovery from demand shocks

• After demand shocks, p ≥ 70% fleets settle within a few steps while p = 40–50% takes approximately 30–40 steps; with forgetting λ ≤ 0.95, convergence after a shock returns within a few steps.Standard fusion with λ = 1 may require hundreds of steps to recover from the shock.Source: §4 · p. 6, Figure 8 · p. 6, Figure 9 · p. 6

• The agent-based realization converges to the macroscopic equilibrium and supports deployment-level findings unavailable to static analysis.Source: §5 · p. 6
• The findings are limited to a single weaving ramp, a calibrated affine-cost model, and homogeneous learning rates.Source: §5 · p. 6
• Future work includes coupled weaving-section networks and heterogeneous or adaptive learning dynamics.Source: §5 · p. 6