This paper explains why consolidation acquisitions occur in waves and it predicts the differing role each firm is likely to play in the consolidation game. We propose that whether a firm assumes the role of rival consolidator, target, or passive observer depends on the position of the firm relative to the entity that merges first. Our model predicts that an initial acquisition triggers a wave of follow-on acquisitions, where the process of asset accumulation by the consolidator is accelerated since the value of follow-on acquisitions is enhanced by the more concentrated industry structure. An initial consolidation can trigger a consolidating acquisition by a rival in a remote market segment, while some firms prefer to be a target and others remain passive observers that await the outcome of the consolidation process rather than merge amongst themselves. Fragmentation, demand uncertainty, and investment costs determine the timing of acquisitions.