Cooperative driving at mixed-traffic unsignalized intersections is challenged by imperfect vehicle-to-everything (V2X) communication, human-driven vehicle (HV) intentions that cannot be directly communicated, and the potential incompatibility of independently generated crossing decisions. This paper proposes State-Intent-Aware Graph Multi-Agent Reinforcement Learning for Cooperative Driving under Imperfect V2X (SIGN-MAPPO) to address these challenges through three coordinated mechanisms. Each decision-eligible connected and automated vehicle (CAV) first reconstructs a receiver-specific traffic graph from its ego state and the peer-state records available to it, from which a shared graph-attention policy generates a raw Stop/Go intention augmented with predicted HV-intent features. CAV intentions are then exchanged through timestamped vehicle-to-vehicle (V2V) messages, and a local conflict-aware arbitration layer converts each CAV's intention into a safe executable action despite potentially inconsistent peer information. In the principal Simulation of Urban MObility (SUMO) evaluation, SIGN-MAPPO achieves a 97.53% completion rate, a 0.10% collision rate, and a mean intersection traversal time of 35.28 s. Ablation studies further confirm the complementary contributions of HV-intent prediction and CAV-intent exchange to this performance. The trained policy also remains robust under the evaluated communication-delay and packet-loss ranges, and cross-scenario tests show complete traffic clearance across the tested settings, though safety margins narrow under compound unpredictable HV behavior.

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