Solidarity, monotonicity, and externalities in cooperative game theory

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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.