The Impact of Cut-ins on Mixed-Autonomy Traffic Flow: Bridging Microscopic Game-Theoretic Model and Macroscopic Flow Analysis

Abstract

The transition to automated transportation introduces mixed-autonomy traffic where human drivers may strategically exploit the risk-averse behavior of Connected and Automated Vehicles (CAVs). While microscopic models capture these dyadic interactions, their aggregate impact on network-level stability remains unquantified due to the scale gap between agent-based and continuum models. This study bridges this analytical divide by integrating a game-theoretic friction term directly into the macroscopic kinematic wave framework. We model the cut-in maneuver as a Stackelberg game, identifying a distinct "exploitation window" where human drivers leverage CAV defensiveness to execute aggressive merges. By deriving a closed-form micro-macro bridge, we translate these discrete strategic outcomes into a continuous friction parameter that endogenously modifies the traffic conservation law. Theoretical analysis and numerical simulations confirm that this behavioral asymmetry functions as a deterministic destabilizer, generating perturbation source terms that trigger phantom jams and strictly reduce road capacity. Crucially, we reveal a convex relationship between CAV penetration and system efficiency, identifying a critical instability regime at intermediate penetration rates (approximately 45 percent) where the frequency of exploitable interactions is maximized. These findings demonstrate that without socially aware control policies, the defensive nature of early-deployment CAVs may paradoxically degrade traffic flow stability.