Solidarity, monotonicity, and externalities in cooperative game theory

近年来，在合作博弈论的研究中，有两个问题引起了人们的广泛关注。第一，团结与绩效导向的协调；第二，外部性的纳入。我们的项目连接到这两方面的研究，并努力结合从两个部分的文献见解。Shapley值可能是合作博弈论中最重要的单值解概念。Shapley值严格以绩效为导向，不考虑外部性。有几种解决方案可以概括Shapley值并考虑到团结的各个方面。特征描述（公理化）允许对这些解决方案的合理性做出更好的判断。同样，对于具有外部性的合作博弈，也存在一些Shapley值的概括。特征描述有助于对这些概括做出更好的判断。现有的推广是基于一个解应该满足线性的假设。然而，DeClippel和Serrano （2008， ECTA）认为，这是一个相当数学化的假设，并不太有说服力。自从Young （1985， IJGT）证明Shapley值可以在没有线性的情况下表征以来，研究者们就试图在没有线性假设的情况下进行研究。Casajus和Huettner （2014， JET）成功地为统一解提供了一个没有线性的表征。在这个项目中，我们的目标是在处理外部性时利用这些见解。我们的目标是描述具有不依赖于线性公理的外部性的合作博弈的既定解决方案。此外，我们寻找已知解决方案概念的进一步基础。我们还将研究在外部性情况下反映团结概念的解决方案概念。此外，稳定集团的形成应在外部性的背景下进行研究。最后，通过调整最近关于无外部性的合作游戏的研究结果，我们将获得新的结构性见解。

Recently, two issues attracted a lot of attention in the literature on cooperative game theory. First, the reconciliation of solidarity and performance orientation and, second, the incorporation of externalities. Our project connects to both lines of research and strives for combining insights from both parts of the literature.The Shapley value probably is the most important single-valued solution concept in cooperative game theory. The Shapley value is strictly performance-oriented and disregards externalities.There exist several solutions that generalize the Shapley value and take into account aspects of solidarity. Characterizations (axiomatizations) allow for a better judgement on the plausibility of these solutions.Similarly, there exist several generalizations of the Shapley value for cooperative games with externalities. Characterizations allow for a better judgement on these generalizations.The existing generalizations are based on the assumption that a solution should satisfy linearity. DeClippel and Serrano (2008, ECTA), however, argue that this is a rather mathematical assumption, which is not too compelling. Ever since Young (1985, IJGT) showed that the Shapley value can be characterized without linearity, researchers tried to do without the assumption of linearity. Casajus and Huettner (2014, JET) succeed to provide a characterization without linearity for solidary solutions. In this project, we aim to make use of these insights when dealing with externalities. We aim for a characterization of established solutions for cooperative games with externalities that do not rely on the linearity axiom. Moreover, we look for further foundations of known solution concepts.We will also study solution concepts that reflect the notion of solidarity in the case of externalities. Further, the formation of stable groups shall be studied in the context of externalities. Finally, new structural insights shall be gained by adapting recent results on cooperative games without externalities.