Agents are normally designed to be self-interested and tend to maximize their own interests in many realistic systems, such as robotics, smart grids and autonomous vehicles. In this paper, we propose a model of repeated bimatrix game to study the ubiquitous group behavior, coalescence, in multi-agent systems, where different agents form a union and keep consensus in states. We find that whether the system can reach coalescence will significantly depend on the payoffs, the functions of the distance between agents’ states. As a result, if the maximum initial distance of agents’ states is sufficiently large, all agents in the population will fail to reach coalescence. If the maximum initial distance remains sufficiently small, on the contrary, all agents will form a union. Moreover, the distribution and the expected value of coalescence time are explicitly obtained when the utility of agents is described by a power function. Finally, simulation examples are provided to validate the effectiveness of the theoretical results.

代理通常被设计为自私的，并且倾向于在许多现实系统中最大化自身利益，例如机器人技术，智能电网和自动驾驶汽车。在本文中，我们提出了一个重复的双矩阵博弈模型，以研究在不同主体形成联盟并保持状态一致的多主体系统中普遍存在的群体行为，合并。我们发现系统能否达到合并将在很大程度上取决于收益，代理状态之间距离的函数。结果，如果主体状态的最大初始距离足够大，则总体中的所有主体将无法达到合并。相反，如果最大初始距离保持足够小，则所有代理将形成并集。此外，当通过幂函数描述代理的效用时，可以明确获得合并时间的分布和期望值。最后，通过仿真实例验证了理论结果的有效性。