We study the properties of the core and other solution concepts of Bel coalitional games, that generalize classical coalitional games by introducing uncertainty in the framework. In this uncertain environment, we work with contracts, that specify how agents divide the values of the coalitions in the different states of the world. Every agent can have different a priori knowledge on the true state of the world, which is modeled through the Dempster-Shafer theory, while agents' preferences between contracts are modeled by the Choquet integral. We focus on the "ex-ante" scenario, when the contract is evaluated before uncertainty is resolved. We investigate the geometrical structure of the ex-ante core when agents have the same a priori knowledge which is a probability distribution. Finally, we define the (pre)nucleolus, the kernel and the bargaining set (a la Mas-Colell) in the ex-ante situation and we study their properties. It is found that the inclusion relations among these solution concepts are the same as in the classical case. Coincidence of the ex-ante core and the ex-ante bargaining set holds for convex Bel coalitional games, at the price of strengthening the definition of bargaining sets.

翻译：我们研究了Bel联盟博弈的核心及其他解概念的性质，该博弈通过引入不确定性框架推广了经典联盟博弈。在此不确定环境中，我们处理契约，这些契约规定了代理人如何在世界的不同状态下分配联盟的价值。每个代理人对世界真实状态可能具有不同的先验知识，这通过Dempster-Shafer理论建模，而代理人对契约的偏好则由Choquet积分建模。我们聚焦于"事前"情景，即在不确定性解决之前评估契约。我们研究了当代理人具有相同先验知识（即概率分布）时，事前核心的几何结构。最后，我们定义了事前情景下的（预）核仁、核及讨价还价集（Mas-Colell式），并研究了它们的性质。研究发现，这些解概念之间的包含关系与经典情形相同。对于凸Bel联盟博弈，事前核心与事前讨价还价集的重合性成立，但需要强化讨价还价集的定义。