A key challenge in distributed coalition formation within characteristic function games is determining how to allocate the calculation of coalition values across a set of agents. The number of possible coalitions grows exponentially with the number of agents, and existing distributed approaches may produce uneven or redundant allocations, or assign coalitions to agents that are not themselves members. In this article, we present the \emph{Necklace-based Distributed Coalition Algorithm} (N-DCA), a communication-free algorithm in which each agent independently determines its own coalition value calculation allocation using only its identifier and the total number of agents. The approach builds on the notion of Increment Arrays (IAs), for which we develop a complete mathematical framework: equivalence classes under circular shifts, periodic IAs, and a rotated designation scheme with formal load-balance guarantees (tight bounds). We establish a bijection between canonical representative IAs and two-colour combinatorial necklaces, enabling the use of efficient necklace generation algorithms to enumerate allocations in constant amortised time. N-DCA is, to the best of our knowledge, the only distributed coalition value calculation algorithm for unrestricted characteristic function games to provably satisfy five desirable properties: no inter-agent communication, equitable allocation, no redundancy, balanced load, and self-interest. An empirical evaluation against DCVC (Rahwan and Jennings 2007) demonstrates that, although DCVC is faster by a constant factor, this difference becomes negligible under realistic characteristic-function evaluation costs, while N-DCA offers advantages in working memory, scalability, and the self-interest guarantee.

翻译：特征函数博弈中的分布式联盟形成面临一个关键挑战：如何将联盟价值的计算任务分配给一组智能体。可能的联盟数量随智能体数量呈指数增长，而现有的分布式方法可能产生不均衡或冗余的分配，或将联盟分配给非成员智能体。本文提出基于项链的分布式联盟算法，这是一种无需通信的算法，每个智能体仅通过其标识符和总智能体数量独立决定其联盟价值计算分配。该方法建立在增量数组的概念之上，我们为其开发了完整的数学框架：循环移位下的等价类、周期型增量数组以及具有形式化负载均衡保证的旋转指定方案。我们在标准型增量数组与双色组合项链之间建立双射，从而能够利用高效的项链生成算法以恒定均摊时间枚举所有分配。据我们所知，N-DCA是首个在无限制特征函数博弈中可证明满足五项理想性质——无需智能体间通信、公平分配、无冗余、负载均衡和自利性——的分布式联盟价值计算算法。与DCVC（Rahwan and Jennings 2007）的实证评估表明，尽管DCVC在常数因子下速度更快，但在实际特征函数计算成本下该差异可忽略不计，而N-DCA在工作内存、可扩展性和自利性保证方面具有优势。