  We consider a sequence of transferable utility (TU) games where, at each
time, the characteristic function is a random vector with realizations
restricted to some set of values. The game differs from other ones in the
literature on dynamic, stochastic or interval valued TU games as it combines
dynamics of the game with an allocation protocol for the players that
dynamically interact with each other. The protocol is an iterative and
decentralized algorithm that offers a paradigmatic mathematical description of
negotiation and bargaining processes. The first part of the paper contributes
to the definition of a robust (coalitional) TU game and the development of a
distributed bargaining protocol. We prove the convergence with probability 1 of
the bargaining process to a random allocation that lies in the core of the
robust game under some mild conditions on the underlying communication graphs.
The second part of the paper addresses the more general case where the robust
game may have empty core. In this case, with the dynamic game we associate a
dynamic average game by averaging over time the sequence of characteristic
functions. Then, we consider an accordingly modified bargaining protocol.
Assuming that the sequence of characteristic functions is ergodic and the core
of the average game has a nonempty relative interior, we show that the modified
bargaining protocol converges with probability 1 to a random allocation that
lies in the core of the average game.
