Emotional expressions and their changes during an interaction affect heavily how we perceive and behave towards other persons. To design an HRI scenario that makes possible to observe, understand, and model affective interactions and generate the appropriate responses or initiations of a robot is a very challenging task. In this paper, we report our efforts in designing such a scenario, and to propose a modeling strategy of affective interaction by artificial intelligence deployed in autonomous robots. Overall, we present a novel HRI game scenario that was designed to comply with the specific requirements that will allow us to develop the next wave of affective-aware social robots that provide adequate emotional responses.