Solidarity and monotonicity in cooperative game theory

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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.