This paper presents a new method for unsupervised video summarization. The proposed architecture embeds an Actor-Critic model into a Generative Adversarial Network and formulates the selection of important video fragments (that will be used to form the summary) as a sequence generation task. The Actor and the Critic take part in a game that incrementally leads to the selection of the video key-fragments, and their choices at each step of the game result in a set of rewards from the Discriminator. The designed training workflow allows the Actor and Critic to discover a space of actions and automatically learn a policy for key-fragment selection. Moreover, the introduced criterion for choosing the best model after the training ends, enables the automatic selection of proper values for parameters of the training process that are not learned from the data (such as the regularization factor $\sigma $ ). Experimental evaluation on two benchmark datasets (SumMe and TVSum) demonstrates that the proposed AC-SUM-GAN model performs consistently well and gives SoA results in comparison to unsupervised methods, that are also competitive with respect to supervised methods.