<p>The importance of gaze in human-robot interaction (HRI) is well documented, particularly for its contribution in regulating turn-taking and managing roles in conversations. However, few gaze models have yet been proposed for multi-party interactions, i.e. several people facing the robot. In this paper, we propose to build and evaluate a gaze control for a robot animating a collaborative game engaging two humans. This model has the particularity of predicting for the robot, both gaze targets and head movements using machine learning algorithms. In this way, we hope to achieve subtle, natural control of eyes-head coordination, which is usually neglected. This model was trained with an original corpus recorded using immersive teleoperation of a robot, providing precise data of a human-like behavior in HRI. Once trained, this model was subjectively evaluated with two online third-person evaluations. The first evaluation shows that the head movements predicted by our model are preferred to those of a heuristic model based purely on the distance between two fixations, and therefore without knowledge of the interaction context. The second evidences that, by biasing the model inputs, the predictions enabled our robot to communicate to whom it speaks (one or both players) simply by controlling its gaze. These results are promising and suggest that this type of model is entirely viable for the generation of gaze behavior in interaction, and that it offers efficient levers for its control.</p>