Cooperative Games with Overlapping Coalitions
Cooperative Games with Overlapping Coalitions
复制标题
DOI：
10.1613/jair.3075
复制
发表时间：
2010-09
期刊：
影响因子：
--
通讯作者：
G. Chalkiadakis;Edith Elkind;E. Markakis;M. Polukarov;N. Jennings
中科院分区：
文献类型：
--
作者：
G. Chalkiadakis;Edith Elkind;E. Markakis;M. Polukarov;N. Jennings
在通常的合作博弈论模型中，联盟形成过程的结果要么是大联盟，要么是由分离联盟组成的联盟结构。然而，在许多联盟与任务相关联的领域中，一个代理可能参与执行多个任务，因此可能会在几个联盟中分配他的资源。为了解决这种情况，我们引入了一个具有重叠联盟的合作博弈模型-或重叠联盟形成（OCF）博弈。然后，我们探讨在这种情况下的稳定性问题。特别地，我们引入了核心的概念，它概括了传统（非重叠）场景中的相应概念。然后，在一些相当一般的条件下，我们描述了核心要素的特征，并证明了核心的任何要素都能最大化社会福利。我们还引入了重叠联盟博弈的平衡概念，并用它来描述可以扩展到核心元素的联盟结构。最后，我们将凸性的概念推广到我们的设置中，并表明在一些自然假设下凸对策具有非空核心。此外，我们在OCF中引入了两种允许更大范围偏差的稳定性替代概念，并探讨了相应核心定义之间的关系，以及经典（非重叠）核心和Aubin核心。我们说明了三个核心的一般性质，并从计算的角度研究它们，从而获得对其基本结构的额外见解。
In the usual models of cooperative game theory, the outcome of a coalition formation process is either the grand coalition or a coalition structure that consists of disjoint coalitions. However, in many domains where coalitions are associated with tasks, an agent may be involved in executing more than one task, and thus may distribute his resources among several coalitions. To tackle such scenarios, we introduce a model for cooperative games with overlapping coalitions-or overlapping coalition formation (OCF) games. We then explore the issue of stability in this setting. In particular, we introduce a notion of the core, which generalizes the corresponding notion in the traditional (non-overlapping) scenario. Then, under some quite general conditions, we characterize the elements of the core, and show that any element of the core maximizes the social welfare. We also introduce a concept of balancedness for overlapping coalitional games, and use it to characterize coalition structures that can be extended to elements of the core. Finally, we generalize the notion of convexity to our setting, and show that under some natural assumptions convex games have a non-empty core. Moreover, we introduce two alternative notions of stability in OCF that allow a wider range of deviations, and explore the relationships among the corresponding definitions of the core, as well as the classic (non-overlapping) core and the Aubin core. We illustrate the general properties of the three cores, and also study them from a computational perspective, thus obtaining additional insights into their fundamental structure.