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An initiative conflict is an overlap of speech in which both conversants try to steer the conversation in different directions. In this paper, we investigate how conversants in human-human dialogue deal with such conflicts. First, in investigating why initiative conflicts occur, we find that the offsets of the utterances involved in initiative conflicts tend to be very short, and that initiative conflicts seem more likely to occur when one of the conversants has an urgent conversational goal. These findings strongly suggest that initiative conflicts are unintentional collisions and that conversants try to prevent them from even occurring, unless there is an urgent reason. Second, in investigating how initiative conflicts are resolved, we find that the overlaps tend to last less than two syllables, that volume correlates with who wins initiative conflicts, and that for longer overlaps, the volume of the winner increases in the second half of the overlaps. These findings strongly suggest that initiative conflicts are quickly resolved through an interactive process, using volume as one of the devices. Third, we find that after an initiative conflict is resolved, the winner sometimes repeats the words involved in the overlap; and this happens more when the overlap is more likely to interfere with the other conversant's understanding. These findings will help us build next-generation mixed-initiative spoken dialogue systems that are natural and efficient to use.