This study focuses on inter-individual convergence effects in the perception and categorization of speech sounds. We ask to what extent two listeners can come to establish a shared set of categorization criteria in a phoneme identification task that they accomplish together. Several hypotheses  are  laid  out  in  the  framework  of  a  Bayesian  model  of  speech  perception  that  we  have  developed  to  account  for  how  two  listeners  may  each  infer  the  parameters  that  govern  their partner’s responses. In our experimental paradigm, participants were asked to perform a joint  phoneme  identification  task  with  a  partner  that,  unbeknownst  to  them,  was  an  artificial  agent, whose responses we manipulated along two dimensions, the location of the categorical boundary and the slope of the identification function. Convergence was found to arise for bias but not for slope. Numerical simulations suggested that lack of convergence in slope may stem from the listeners’ prior level of confidence in the variance in VOT for the two phonemic categories. This study sheds new light on perceptual convergence between listeners in the categorization of speech sounds, a phenomenon that has received little attention so far in spite of its central importance for speech communication.