Stable solutions of grand coalitions in unbalanced cooperative games

With the rapid development of the digital economy, game theory, as one of its foundational theories, is encountering new opportunities for development. Due to its emphasis on collective rationality, cooperative game theory is widely applied to issues concerning cooperation. However, many cooperative games' cores are empty, namely, the so-called non-balanced games, which leads to instability in grand coalitions. Therefore, studying non-balanced games and finding their stable solutions is crucial for the development and application of cooperative game theory. In this paper, we first systematically review the research on stable solutions in grand coalitions both domestically and internationally, and categorize the research in this field into two perspectives: relaxation of external constraints and modification of internal structures. Furthermore, based on the types of relaxed constraints, we divide the research from the perspective of relaxation of external constraints into two categories: relaxation of budget balance constraints and relaxation of coalition stability constraints. Regarding the modified structural types, the research from the perspective of modification of internal structures is divided into two categories: considering authority structure restrictions and considering coefficient structure adjustments. Finally, we propose two research prospects from both theoretical and practical perspectives: finding new methods to construct stable solutions in grand coalitions and addressing real-world issues of unbalanced games with stronger applicability.