The main ambition of this thesis is to contribute to the development of cooperative game theory towards combinatorics, algorithmics and discrete geometry. Therefore, the first chapter of this manuscript is devoted to highlighting the geometric nature of the coalition functions of transferable utility games and spotlights the existing connections with the theory of submodular set functions and polyhedral geometry. To deepen the links with polyhedral geometry, we define a new family of polyhedra, called the basic polyhedra, on which we can apply a generalized version of the Bondareva-Shapley Theorem to check their nonemptiness. To allow a practical use of these computational tools, we present an algorithmic procedure generating the minimal balanced collections, based on Peleg's method. Subsequently, we apply the generalization of the Bondareva-Shapley Theorem to design a collection of algorithmic procedures able to check properties or generate specific sets of coalitions. In the next chapter, the connections with combinatorics are investigated. First, we prove that the balanced collections form a combinatorial species, and we construct the one of k-uniform hypergraphs of size p, as an intermediary step to construct the species of balanced collections. Afterwards, a few results concerning resonance arrangements distorted by games are introduced, which gives new information about the space of preimputations and the facial configuration of the core. Finally, we address the question of core stability using the results from the previous chapters. Firstly, we present an algorithm based on Grabisch and Sudh\"olter's nested balancedness characterization of games with a stable core, which extensively uses the generalization of the Bondareva-Shapley Theorem introduced in the second chapter. Secondly, a new necessary condition for core stability is described, based on the application ...

翻译：本论文的主要目标是为合作博弈论在组合学、算法学及离散几何方向的发展做出贡献。为此，手稿第一章致力于揭示可转移效用博弈中联盟函数的几何本质，并重点阐明其与子模集合函数理论及多面体几何之间的现有联系。为深化与多面体几何的关联，我们定义了一类新的多面体族——基本多面体，并对其应用Bondareva-Shapley定理的广义版本以检验其非空性。为实现这些计算工具的实际应用，我们基于Peleg方法提出了一种生成极小平衡族系的算法流程。随后，我们将Bondareva-Shapley定理的推广形式应用于设计一系列算法流程，以检验联盟的属性或生成特定集合。在下一章中，我们探讨了与组合学的联系。首先证明平衡族系构成一种组合物种，并作为构造平衡族系物种的中间步骤，构建了大小为p的k-均匀超图的物种。此后，我们引入若干关于博弈扭曲共振排列的结果，为预核空间及核心的面配置提供了新信息。最后，我们利用前文结果讨论核心稳定性问题：首先提出一种基于Grabisch与Sudhölter关于稳定核心博弈的嵌套平衡性表征的算法，该算法广泛运用第二章引入的Bondareva-Shapley定理推广形式；其次描述了一种基于应用...的核心稳定性新必要条件。