确定核的非空性的复杂性
Complexity of Determining Nonemptiness of the Core
摘要：
联盟形成是自利Agent之间自动协商以及其他多Agent应用中的一个关键问题。代理人的联盟有时可以完成单个代理人无法完成的事情，或者可以更有效地完成事情。然而，激励代理人遵守一个解决方案需要仔细分析：只有一些解决方案是稳定的，在这个意义上，没有一组代理人有动机脱离并形成新的联盟。这种约束在合作博弈论中得到了广泛的研究。然而，围绕这一约束的计算问题受到的关注较少。当涉及到软件代理（代表真实世界的各方）之间的联盟形成时，这些问题变得越来越明显。在本文中，我们定义了一个简洁的一般表示游戏的特征形式，依赖于超可加性，并表明，它允许有效的检查是否一个给定的结果是在核心。然后，我们表明，确定核心是否是非空的是$\mathcal{NP}$ -完全的，没有可转移的效用。我们证明，在这两种情况下，是什么使问题很难确定合作的可能性（一组可能的结果，大联盟），通过显示，如果这些都是给定的，问题变得易于处理在这两种情况下。然而，我们然后证明，对于混合版本的问题，效用转移是可能的，只有在大联盟内，问题仍然是$\mathcal{NP}$ -完整的，即使当协作的可能性。
英文摘要：
Coalition formation is a key problem in automated negotiation among self-interested agents, and other multiagent applications. A coalition of agents can sometimes accomplish things that the individual agents cannot, or can do things more efficiently. However, motivating the agents to abide to a solution requires careful analysis: only some of the solutions are stable in the sense that no group of agents is motivated to break off and form a new coalition. This constraint has been studied extensively in cooperative game theory. However, the computational questions around this constraint have received less attention. When it comes to coalition formation among software agents (that represent real-world parties), these questions become increasingly explicit. In this paper we define a concise general representation for games in characteristic form that relies on superadditivity, and show that it allows for efficient checking of whether a given outcome is in the core. We then show that determining whether the core is nonempty is $\mathcal{NP}$-complete both with and without transferable utility. We demonstrate that what makes the problem hard in both cases is determining the collaborative possibilities (the set of outcomes possible for the grand coalition), by showing that if these are given, the problem becomes tractable in both cases. However, we then demonstrate that for a hybrid version of the problem, where utility transfer is possible only within the grand coalition, the problem remains $\mathcal{NP}$-complete even when the collaborative possibilities are given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
