The coalitional Nash bargaining solution with simultaneous payoff demands

We consider a standard coalitional bargaining game where once a coalition forms it exits as in Okada (2011), however, instead of alternating offers, we have simultaneous payoff demands. We focus in the producer game he studies. Each player is chosen with equal probability. If that is the case, she can choose any coalition she belongs to. However, a coalition can form if an only if payoff demands are feasible as in the Nash (1953) demand game. After smoothing the game (as in Van Damme (1991)), when the noise vanishes, when the discount factor is close to 1, and as in Okada's (2011), the coalitional Nash bargaining solution is the unique stationary subgameperfect equilibrium.