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下，评分（特征）函数决定了任意代理子集/联盟的价值。代理需要同时决策联盟的形成方式以及联盟价值在其成员间的分配方案。联盟博弈的核心概念是核解——一种将代理划分为联盟并赋予每个代理相应分配的方案，使得任何代理子群都无法通过组建替代联盟获得更高分配。本文提出了可收敛至核解（若存在）的分布式学习动力学。在该动力学中，每个代理维护包含以下两项的状态：（i）自身分配的期望水平，及（ii）所属联盟（如有）。在每个阶段，随机激活的代理提出组建新联盟，并根据提案成败调整自身期望值。当提案成功时，联盟成员结构相应更新。所需通信包括：（i）新联盟中的候选代理需向提案代理披露当前期望值；（ii）代理需获知其是否加入拟议联盟或原有联盟是否被解散。提案代理负责计算组建联盟的可行性。研究表明，当达到核解时，该动力学将进入吸收态。我们进一步在多智能体任务分配场景中验证了该分布式学习动力学的有效性。