Bargaining theory has a conceptual dichotomy at its core: according to one view, the utilities in the bargaining problem are meaningless numbers (v-N.M utilities), while according to another view they do have concrete meaning (willingness to pay). The former position is assumed by the Nash and...

A bargaining solution guarantees minimal equity if each player's payoff is at least as large as the minimum of the payoffs assigned to him by the equal-gain (i.e., egalitarian) and equal-loss solutions. The Kalai-Smorodinsky solution is the unique scale-invariant 2-person solution with this...

A bargaining solution balances fairness and efficiency if each player's payoff lies between the minimum and maximum of the payoffs assigned to him by the egalitarian and utilitarian solutions. In the 2-person bargaining problem, the Nash solution is the unique scale-invariant solution satisfying...

I characterize the proportional N-person bargaining solutions by individual rationality, translation invariance, feasible set continuity, and a new axiom - interim improvement. The latter says that if the disagreement point d is known, but the feasible set is not - it may be either S or T, where...