Rational Bargaining: Characterization and Implementation

The von Neumann-Morgenstern axioms are uncontroversial desiderata for individual decision-making. We say that a bargaining solution is rational if it can be interpreted as the most preferred alternatives under these axioms. Yet, neither the Nash nor the Kalai-Smorodinsky bargaining solution is rational in this sense. We formalize two consequences of rationality, namely that one can neither be strictly better off nor strictly worse off from randomizing over different actions. These two axioms, together with other standard axioms, characterize the relative utilitarian bargaining solution. We then implement this bargaining solution in sub-game perfect equilibrium.