Why do lions get the lion's share? A Hobbesian theory of agreements

We propose a new bargaining solution, based on the idea - borrowed from Hobbes - that the agreement reached in a negotiation should be determined by how the direct conflict resulting from disagreement would be resolved. The explicit modeling of the disagreement game directly leads to the observation that the outcome of conflict is a function of the stakes. Thus, our basic building block is the disagreement function, which maps each set of feasible agreements into a disagreement point. Using this function and a weakening(!) of the Independence of Irrelevant Alternatives axiom, based on individual rationality, we reach a unique solution. The main feature of the solution is that it is reached via a sequence of partial agreements. We also give two alternative characterizations; one based on a multi-stage, strategic game and one on renegotiation.