Mergers and Acquisitions (M&As) are important business strategies in any industry, as they allow the parties involved to achieve, for example, higher market share, profits and influence in one or more industries. In any M&A activity, the key challenge for an acquirer company is to select the target company that can most improve its performance through synergy. The goal of this research is thus to help acquirer companies model and optimally solve their merger target selection problems (MTSPs) in both horizontal integration and vertical integration settings. We apply both a data envelopment analysis (DEA) based performance evaluation framework and the Nash bargaining solution concept to mathematically model an acquirer company's MTSPs under the two types of integration settings. To the best of our knowledge, the proposed new models are the first DEA-based Nash bargaining models in the literature to help acquirer companies obtain their most desired target companies. Finally, this research provides numerical examples, including real-life examples, to illustrate various aspects and implementation details of the two types of models.