Bargaining, interdependence, and the rationality of fair division

We consider two-person bargaining games with interdependent preferences and bilateral incomplete information. We show that in both the ultimatum game and the two-stage alternating-offers game, our equilibrium predictions are consistent with a number of robust experimental regularities that falsify the standard game-theoretic model: occurrence of disagreements, disadvantageous counteroffers, and outcomes that come close to the equal split of the pie. In the context of infinite-horizon bargaining, the implications of the model pertaining to fair outcomes are even stronger. In particular, the Coase property in our case generates "almost" 50-50 splits of the pie, almost immediately. The present approach thus provides a positive theory for the frequently encountered phenomenon of the 50-50 division of the gains from trade.