1. By transferring 1 unit of good f to player 3, player 1 makes sure that (�, 0, 1/2) is necessarily the outcome of {2, 3}-so this is the optimal threat of player 1 in coalition {1, 2, 3}. Thus the unique SP equilibrium payoffs for the grand coalition are (1/3, 0, 2/3) as seen above;) is always feasible for {2, 3} (even without any transfers)
2. Our point, however, is more general. In the example above player 1, by using a suitable threat (which is not a damaging threat), can alter-to his advantage-the relative bargaining powers of players 2 and 3 in the subsequent negotiation. In the general NTU case, where the specific subsequent agreement of a coalition of players matters to the proposer (whereas in the TU case only the sum of payoffs matters to him), this is bound to be pervasive. From a different perspective, we can view the analysis just made as underlying the existence of a substantial theoretical gap between the TU and the NTU situations. One cannot take for granted that the interesting phenomena that may hold for the former will carry over to the latter (for a different question-the equivalence principle-we made a similar point in Hart and Mas-Colell, 1996b);conclusion, strategic market games, a classical instance of the so-called c-games, are not really c-games: one cannot simply define the coalitional function as what a coalition can do with the total endowment of its members
3. Acceptable Points in General Cooperative n-Person Games;R J Aumann;Contributions to the Theory of Games IV, Annals of Mathematics Study,1959
4. Noncooperative Models of Bargaining;K Binmore;Handbook of Game Theory, with Economic Applications,1992