The core is a central solution concept in cooperative game theory, defined as the set of feasible allocations or payments such that no subset of agents has incentive to break away and form their own subgroup or coalition. However, it has long been known that the core (and approximations, such as the least-core) are hard to compute. This limits our ability to analyze cooperative games in general, and to fully embrace cooperative game theory contributions in domains such as explainable AI (XAI), where the core can complement the Shapley values to identify influential features or instances supporting predictions by black-box models. We propose novel iterative algorithms for computing variants of the core, which avoid the computational bottleneck of many other approaches; namely solving large linear programs. As such, they scale better to very large problems as we demonstrate across different classes of cooperative games, including weighted voting games, induced subgraph games, and marginal contribution networks. We also explore our algorithms in the context of XAI, providing further evidence of the power of the core for such applications.

翻译：核心是合作博弈理论中的核心解概念，定义为所有可行分配或支付的集合，使得没有任何代理子集有动机脱离并形成自己的子群或联盟。然而，长期以来人们已知核心（以及近似解，如最小核心）难以计算。这限制了我们在一般情况下分析合作博弈的能力，也难以充分利用合作博弈理论在可解释人工智能（XAI）等领域的贡献——在该领域中，核心可补充沙普利值，以识别支持黑箱模型预测的关键特征或实例。我们提出新颖的迭代算法来计算核心的各种变体，这些算法避免了其他许多方法的计算瓶颈，即求解大型线性规划。因此，正如我们在不同类别合作博弈（包括加权投票博弈、诱导子图博弈和边际贡献网络）中所展示的，它们能更好地扩展至超大规模问题。我们还探讨了算法在XAI背景下的应用，为核心在此类应用中的强大作用提供了进一步证据。