In a model of a duopolistic product market with a unionized labor force, this paper explores the interaction between firms' duopolistic behavior and union-firm bargaining. In a two-union/two-firm setting, we show that adopting efficient bargaining can improve a firm's competitiveness as well as efficiency, and it arises in equilibrium; while in a one-union/two-firm set-up, we find that an industry union prefers wage bargaining. However, when foreign competition in the product market intensifies, even the industry union prefers efficient bargaining. As an application, the analysis may explain differences in international competitiveness and the recent trend toward labor-management cooperation in the labor market.