In this paper, a general resource distribution game with a hierarchical structure on the bipartite graph is proposed. In this system, the game is divided into two interacting levels, the agent level and the group level, with negotiations taking place on both levels. Each agent can belong to multiple groups, resulting in a system topology with a bipartite structure. On the agent level, decisions are based on the greedy principle, with the game being a state-based potential game. In contrast, some participants on the group level behave more “smartly” and are more likely to adopt a sophisticated strategy maximizing their personal interest. Strategies on both levels are based on distributed protocols, and the social welfare increases as the system approaches a Nash-equilibrium point. The designed protocols are theoretically analyzed from stability and efficiency. Furthermore, a reinforcement learning algorithm is introduced in the group level, where the smarter players are allowed to refine their strategies in the multi-step decision-making process by learning from historic game outcomes. In theory and according to simulations, agents with the learning behavior improve not only their personal interest but also the efficiency of the systemic resource distribution.

本文提出了一种在二部图上具有层次结构的通用资源分配博弈。在此系统中，游戏分为两个交互级别，即代理级别和组级别，并且在两个级别上进行协商。每个代理可以属于多个组，从而导致系统拓扑具有二分结构。在代理人级别，决策基于贪婪原则，该博弈是基于状态的潜在博弈。相比之下，小组级别上的一些参与者表现得更“聪明”，并且更有可能采用复杂的策略来最大化他们的个人兴趣。这两个级别的策略都基于分布式协议，并且随着系统接近Nash平衡点，社会福利也会增加。从稳定性和效率上对所设计的协议进行了理论分析。此外，在小组级别引入了强化学习算法，通过从历史游戏结果中学习，允许更聪明的玩家在多步决策过程中完善自己的策略。从理论上并根据模拟，具有学习行为的主体不仅可以提高他们的个人兴趣，而且可以提高系统资源分配的效率。