With the practical implementation of connected and autonomous vehicles (CAVs), the traffic system is expected to remain a mix of CAVs and human-driven vehicles (HVs) for the foreseeable future. To enhance safety and traffic efficiency, the trajectory planning strategies of CAVs must account for the influence of HVs, necessitating accurate HV trajectory prediction. Current research often assumes that human drivers have perfect knowledge of all vehicles' objectives, an unrealistic premise. This paper bridges the gap by leveraging hypergame theory to account for cognitive and perception limitations in HVs. We model human bounded rationality without assuming them to be merely passive followers and propose a hierarchical cognition modeling framework that captures cognitive relationships among vehicles. We further analyze the cognitive stability of the system, proving that the strategy profile where all vehicles adopt cognitively equilibrium strategies constitutes a hyper Nash equilibrium when CAVs accurately learn HV parameters. To achieve this, we develop an inverse learning algorithm for distributed intention interpretation via vehicle-to-everything (V2X) communication, which extends the framework to both offline and online scenarios. Additionally, we introduce a distributed trajectory prediction and planning approach for CAVs, leveraging the learned parameters in real time. Simulations in highway lane-changing scenarios demonstrate the proposed method's accuracy in parameter learning, robustness to noisy trajectory observations, and safety in HV trajectory prediction. The results validate the effectiveness of our method in both offline and online implementations.

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