With the rapid development of the Internet, cloud storage has penetrated into every aspect of human society. However, cloud data disclosure happens more and more frequently, which makes cloud data security and privacy protection impact wide adoption of cloud storage. Control cloud data access based on reputation by introducing a Reputation Center (RC) was proposed and demonstrated to secure cloud data effectively in [9] . But the acceptance of such a system by cloud users and Cloud Service Providers (CSPs) is crucial for its practical deployment and final success. In this paper, we investigate the acceptance of a cloud data access control system based on reputation using Game Theory. Due to the existence of dishonest CSPs, there exists a social reputation dilemma among CSPs, which seriously impedes the popularity of cloud storage. To encourage users to use cloud storage and suppress collusion between CSPs and data requesters, a repeated public-goods game is built up by applying a compensation mechanism to improve the utilities of cloud users and a punishment mechanism based on reputation to incent honest behaviors. Theoretical analysis and simulation results show the effectiveness of the compensation and punishment mechanisms to increase cloud storage rate and restrain dishonest system entities.