In this work, a game-theoretic analysis of a video exchange application in which two users exchange their video streams over a satellite channel using Quality of Experience (QoE) driven rate adaptation is studied. In such an interaction, users aim at maximizing the Quality of Service (QoS) and QoE of their received video while minimizing their individual cost incurred by their video transmission, which is modeled as a repeated game. Given the payoff model of the users, it is shown that adaptive video exchange between selfish autonomous nodes for a deterministic time will not be sustained. However, if video is exchanged over an unlimited or indeterminate period, the nodes have an incentive to cooperate and exchange video streams with QoE-driven rate adaptation based on the trust they build among themselves. Our simulation results show that a tradeoff exists between the QoS and the QoE of the perceived video. Furthermore, it is shown that the expected interaction length has a high impact on such tradeoff.