Transferable utility games with uncertainty

We introduce the concept of a transferable utility game with uncertainty (TUU-game). In a TUU-game there is uncertainty regarding the payoffs of coalitions. One out of a finite number of states of nature may materialize and conditional on the state, the players are involved in a particular transferable utility game. We consider the case without ex ante commitment possibilities and propose the Weak Sequential Core as a solution concept. We characterize the Weak Sequential Core and show that it is non-empty if all ex post TU-games are convex. We study bankruptcy games with uncertainty and apply the Weak Sequential Core. We find that most of the best-known allocation rules are unstable in this setting, except for the Constrained Equal Awards rule