In the framework of transferable utility coalitional games, a scoring (characteristic) function determines the value of any subset/coalition of agents. Agents decide on both which coalitions to form and the allocations of the values of the formed coalitions among their members. An important concept in coalitional games is that of a core solution, which is a partitioning of agents into coalitions and an associated allocation to each agent under which no group of agents can get a higher allocation by forming an alternative coalition. We present distributed learning dynamics for coalitional games that converge to a core solution whenever one exists. In these dynamics, an agent maintains a state consisting of (i) an aspiration level for its allocation and (ii) the coalition, if any, to which it belongs. In each stage, a randomly activated agent proposes to form a new coalition and changes its aspiration based on the success or failure of its proposal. The coalition membership structure is changed, accordingly, whenever the proposal succeeds. Required communications are that: (i) agents in the proposed new coalition need to reveal their current aspirations to the proposing agent, and (ii) agents are informed if they are joining the proposed coalition or if their existing coalition is broken. The proposing agent computes the feasibility of forming the coalition. We show that the dynamics hit an absorbing state whenever a core solution is reached. We further illustrate the distributed learning dynamics on a multi-agent task allocation setting.

翻译：在可转移效用联盟博弈框架中，评分（特征）函数决定了任意代理子集/联盟的价值。代理需要同时决定形成哪些联盟，以及所形成联盟的价值如何在成员间分配。联盟博弈中的一个重要概念是核解，即一种将代理划分为联盟的结构，并为每个代理分配相应收益，使得任何代理群体都无法通过组建替代联盟获取更高收益。我们提出了分布式学习动力学，该机制能在核解存在时收敛至该解。在这些动力学过程中，每个代理维护一个包含以下两项的状态：(i) 对其分配收益的期望水平，(ii) 所属的联盟（如果有）。在每个阶段，随机选中的代理提议组建新联盟，并根据提议成功与否调整其期望值。当提议成功时，联盟成员结构相应改变。所需通信包括：(i) 拟议新联盟中的代理需向提议代理披露其当前期望值，(ii) 代理需获知自己是否加入拟议联盟或是否原联盟被解散。提议代理计算组建联盟的可行性。我们证明，一旦达到核解，该动力学过程将进入吸收态。我们进一步在多代理任务分配场景中展示了该分布式学习动力学的运行机制。