With ever greater amounts of data stored in cloud servers, data security and privacy issues have become increasingly important. Public cloud storage providers are semi-trustworthy because they may not have adequate security mechanisms to protect user data from being stolen or misused. Therefore, it is crucial for cloud users to evaluate the security of cloud storage providers. However, existing security assessment methods mainly focus on external security risks without considering the trustworthiness of cloud providers. In addition, the widely used third-party mediators are assumed to be trusted and we are not aware of any work that considers the security of these mediators. This study fills these gaps by assessing the security of public cloud storage providers and third-party mediators through equilibrium analysis. More specifically, we conduct evaluations on a series of game models between public cloud storage providers and users to thoroughly analyze the security of different service scenarios. Using our proposed security assessment, users can determine the risk of whether their privacy data is likely to be hacked by the cloud service providers; the cloud service providers can also decide on strategies to make their services more trustworthy. An experimental study of 32 users verified our method and indicated its potential for real service improvement.