The Tradewise-Function Form for Transferable Utility Games

We introduce a new cooperative game form called the cooperative game in the tradewise-function form and denote it Γ . In Γ , we consider allocations that encompass the players' payoff and the coalitional structure they form. The set of feasible allocations is restricted to t-feasible allocations, those we can expect to result, at any step of a coalition formation process, from the optimal cooperative behavior of the players. We show that the core of Γ is non-empty and coincides with the set of Pareto optimal allocations of Γ and with the set of t-feasible allocations that cannot be t-extended by any t-feasible allocation. Moreover, the cores of the characteristic-function and the tradewise-function forms coincide when the first is not empty. Hence, when the core in the characteristic-function form is not empty, whether we consider all the feasible allocations or only the t-feasible allocations is irrelevant to the final outcome. However, our theory also provides a prescription, in the same spirit, for games in which the core of the characteristic-function form is empty.