Solidarity and monotonicity in cooperative game theory

最近，团结和绩效导向的协调在合作博弈论的文献中引起了很多关注。我们的项目有助于这项研究计划。Shapley值（Shapley 1953）可能是合作博弈论中最重要的单值解概念。Young（1985）指出Shapley解的特征在于三个经济上合理的公理：有效性、对称性和强单调性。虽然效率和对称性是相当“无害”的标准公理，但强单调性反映了Shapley值的严格性能取向。代替强单调性公理，货车den Brink等人（2013）考虑了弱单调性公理。这种弱单调性公理允许一方面将联合收割机性能取向与另一方面的团结考虑相结合。然而，迄今为止，弱单调性公理的含义还没有得到充分的探讨。这是这个项目的首要目标。社会群体的形成是社会科学中的一个重要问题。在合作博弈论中，人们试图通过稳定性的考虑来解释群体的形成。在这些努力中，尚未考虑到行为者之间的团结。在这个项目中，我们研究团结是否以及在多大程度上促进了群体的形成。最后，Shapley解及其特征构成了许多其他应用和分配规则的基础。在这个项目中，我们通过团结的透镜来看待已建立的应用程序。

Recently, the reconciliation of solidarity and performance orientation attracted a lot of attention in the literature of cooperative game theory. Our project contributes to this research program. The Shapley value (Shapley 1953) probably is the most important single-valued solution concept of cooperative game theory. Young (1985) shows that the Shapley solution is characterized by three economically sound axioms: efficiency, symmetry, and strong monotonicity. While efficiency and symmetry are rather "innocuous" standard axioms, strong monotonicity reflects the strict performance orientation of the Shapley value. Instead of the strong monotonicity axiom, van den Brink et al. (2013) consider a weak monotonicity axiom. This weak monotonicity axiom allows to combine performance orientation on the one hand and solidarity considerations on the other hand. However, the implications of the weak monotonicity axiom have not sufficiently been explored so far. To do this is the first aim of this project. The formation of groups within the society is an important question in social sciences. In cooperative game theory, attempts have been made to explain the formation of groups by help of stability considerations. Within these attempts, solidarity among the players has not yet been taken into account. In this project, we examine whether and to what extent solidarity promotes the formation of groups. Finally, the Shapley solution and its characterizations form the basis for many other applications and allocation rules as well as their foundations. In this project, we look at established applications through the lens of solidarity.