This paper explores the possibility of using evolutionary algorithms (EAs) to automatically generate efficient and stable strategies for complicated bargaining problems. This idea is elaborated by means of case studies. We design artificial players whose learning and self-improving capabilities are powered by EAs, while neither game-theoretic knowledge nor human expertise in game theory is required. The experimental results show that a co-evolutionary algorithm (CO-EA) selects those solutions which are identical or statistically approximate to the known game-theoretic solutions. Moreover, these evolved solutions clearly demonstrate the key game-theoretic properties on efficiency and stability. The performance of CO-EA and that of a multi-objective evolutionary algorithm (MOEA) on the same problems are analyzed and compared. Our studies suggest that for real-world bargaining problems, EAs should automatically design bargaining strategies bearing the attractive properties of the solution concepts in game theory.