By imputation and core I mean the terms from game theory.
An imputation is a payoff vector satisfying the efficiency and individual rationality conditions and the core is the set of allocations vectors satisfying the efficiency and stability condition.
A cooperative game (Tu Game) can be considered as a stylized bargaining process. Thus, an element of the imputation set or the core or any other solution concept can be interpreted as indicating a proposal (or outcome from a negotiation process) of how one should distribute the gains of mutual cooperation by the grand coalition, if the agents accept the rules of distributive justice related to the core/imputation or any other solution (set of axioms). If the core exists, a core element proposal can be stabilized on the ground that one can not find any coalition that could block this proposal. Notice, in addition, there is no need for a binding agreement here. It is enough to claim that the agents have agreed upon on the set of principles of distributive arbitration related to the core (axioms). In this context, it is important to notice that if something is assumed to be binding, it makes no sense to claim that one can deviate from it. If the core is empty, the fact is more complicated. However, in this case, we can look if such an imputation (proposal/agreement) can be stabilized on the ground of the stable set or bargaining set. But then we cannot expect anymore an agreement into the grand coalition. For more details see my book Meinhardt (2013), Chap. 3 & 4.
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