Returns to costly pre-bargaining claims: taking a principled stand

We construct a 'divide the dollar' bargaining game which formalizes Schelling's notion of a 'qualitative commitment'. This requires a substantial capitulation cost to be incurred -- discontinuously -- if and only if a player accepts a share of an asset below his pre-announced 'claim' on it, no matter how little below. The 'commitment game' opens with an 'announcement round' in which the two players simultaneously announce their claims on the asset, and is followed by a Rubinstein alternating-offers 'negotiation subgame'. We determine the unique subgame-perfect, stationary, pure-strategy equilibrium outcome of the commitment game and find it to be efficient. The main feature of the model is that gains, relative to the game without commitment, do result to the first-mover provided the capitulation cost is above a certain threshold. The more the capitulation cost exceeds the threshold, the greater is the gain. The higher the impatience level of the players, the higher the stakes need to be