In dialogue, it is not uncommon for people to laugh together. This joint laughter often results in overlapping laughter, consisting of an initiating laugh (the first one), and a responding laugh (the second one). In previous studies, we found that overlapping laughs are acoustically different from non-overlapping ones. So far, we have considered overlapping laughs as one category. Consequently, it is unknown whether there are also acoustic differences between initiating laughs and responding laughs. In this paper, we make a distinction between initiating, responding, and non-overlapping laughs and compare their acoustic characteristics. In particular, we will investigate the prosodic relations between initiating and responding laughs. Do these relations point to a form of accommodation and mimicry? To what extent are initiating and responding laughs paired to each other? The analyses were performed on two speech corpora containing spontaneous conversations between two speakers. Results show indications that initiating and responding laughs share several similar acoustic features that point towards accommodation and mimicry mechanisms.