Virtual agents are increasingly being used for communication training such as public speaking-, job interviews-, as well as negotiation training. In these use-cases the agent is generally taking on the role of interviewer and its behaviour is altered according to the nonverbal cues of its human interlocutor. However, understanding how the agent's non-verbal cues influence human behaviour, perception or interactions outcomes is equally important. This contributes to appropriate behaviour generation in agents, but also to our understanding of the intricate interplay of non-verbal behaviours on human perception and interaction outcomes. This study focuses specifically on the perception of vocal dominance in human-agent negotiation. Earlier research showed that the perception of dominance influences decision making in the course of negotiations, as do concessions tactics. However, the effect of voice as well as the effect of the negotiator type in this regard have been so far under-explored. To close this gap, an online experiment was conducted, in which a total number of 121 participants negotiated with conversational agents displaying either low or high vocal dominance, and an individualistic or neutral concession tactic. The results showed that when taking into account the self-reported type of negotiator, significant differences caused by vocal dominance were evident in regard to the number of negotiation rounds and perceived fairness. The number of rounds was significantly higher for the competitive participant type negotiating with the low vocal dominance agent, and the perceived fairness was significantly lower with the collaborative participant type negotiating with the high vocal dominance agent.