A system-theoretic model for cooperative settings is presented that unifies and ex-
tends the models of classical cooperative games and coalition formation processes and
their generalizations. The model is based on the notions of system, state and transi-
tion graph. The latter describes changes of a system over time in terms of actions
governed by individuals or groups of individuals. Contrary to classic models, the pre-
sented model is not restricted to acyclic settings and allows the transition graph to have
cycles.
Time-dependent solutions to allocation problems are proposed and discussed. In par-
ticular, Weber’s theory of randomized values is generalized as well as the notion of
semi-values. Convergence assertions are made in some cases, and the concept of the
Cesàro value of an allocation mechanism is introduced in order to achieve convergence
for a wide range of allocation mechanisms. Quantum allocation mechanisms are de-
fined, which are induced by quantum random walks on the transition graph and it is
shown that they satisfy certain fairness criteria. A concept for Weber sets and two dif-
ferent concepts of cores are proposed in the acyclic case, and it is shown under some
mild assumptions that both cores are subsets of the Weber set.
Moreover, the model of non-cooperative games in extensive form is generalized such
that the presented model achieves a mutual framework for cooperative and non-co-
operative games. A coherency to welfare economics is made and to each allocation
mechanism a social welfare function is proposed
