Cloud storage technology offers users significant convenience. However, the presence of large volumes of redundant data leads to wasted storage resources, highlighting the necessity of data deduplication. Simultaneously, to safeguard user privacy, secure deduplication of encrypted data must be implemented, which increases the computational overhead associated with cloud storage. Consequently, substantial research efforts have been directed toward secure deduplication. In prior work, scholars introduced a secure deduplication method based on autoencoder models, effectively reducing the computational overhead of the Random Message-Locked Encryption (R-MLE) deduplication scheme. Nevertheless, this approach requires users to generate the autoencoder model, thereby increasing their computational costs. To address this issue, this paper introduces a third-party server (TPS) to assist users in generating the autoencoder model, thereby reducing their computational costs. Furthermore, two game-theoretic models, namely ‘User-Cloud Service Provider (CSP)’ and ‘TPS-CSP’ have been developed to simulate participant behavior within the new secure deduplication framework. Experimental results demonstrate that the proposed scheme enhances both the number of user engagement and CSP profits compared to traditional R-MLE-based and autoencoder-based schemes.