This paper introduces CRAVE (Conversational Recommendation Agents with Collaborative Verbalized Experience), a novel framework designed to enhance Large Language Model (LLM)-based conversational recommender systems (CRSs). The core idea is to improve recommendation accuracy by leveraging implicit, personalized, and agent-specific experiences derived from historical user interactions. CRAVE achieves this by sampling trajectories of LLM agents on past queries and creating "verbalized experience banks" based on user feedback. A collaborative retriever network then helps identify relevant, preference-oriented experiences for new queries, further augmented by a debater-critic agent (DCA) system that encourages diverse recommendations through a structured debate. The research demonstrates that this approach significantly outperforms existing zero-shot LLM methods and other baselines, particularly when augmented with collaborative verbalized experience.