We introduce a new class of cooperative games where the worth of a coalition
depends on the behavior of other players and on the state of nature as well. We
allow for coalitions to form both before and after the resolution of uncertainty, hence
agreements must be stable against both types of deviations. The appropriate exten-
sion of the classical core concept, the Sustainable Core, is defined for this new setup
to test the stability of allocations in such a complex environment.
A prominent application, a game of consumers and generators on an electrical
energy transmission network is examined in details, where the power in and outlets
of the nodes have to be determined in a way, that if any line instantaneously fails,
none of the remaining lines may be overloaded. In the case of a line failure, stability
may be lost, and the network has to be brought to a stable state again via the
rescheduling of generators and curtailment of loads. This affects the energy transfer
between cooperating players. We show that fulfilling this safety requirement can be
achieved by choosing an element in the Sustainable Core.