We present a novel experimental design that combines highly accurate psychometric methods with an interactive task to characterize how two or more listeners can converge towards each other in the categorization of speech sounds. The design is implemented as a cooperative game, in which listeners are presented with a sequence of sounds that range on a continuum between two endpoints unambiguously associated with two phoneme categories in a joint phoneme identification task. To play the game successfully, listeners must comply with both a distinctivity constraint (identify the endpoints as being different from each other) and an agreement constraint (identify the stimuli in the same way as their partner). Our first results show that our experimental design opens new avenues for research on convergence between listeners in speech perception.