Volker Britz Optimal Value Commitment in Bilateral

We propose a new model to study the role of commitment as a source of strategic bargaining power. Two impatient players bargain about the division of a pie under a standard bargaining protocol in discrete time with time-invariant recognition probabilities. Instantaneous utility is linear, but players discount the future by a constant factor. Before bargaining starts, a player can commit not to enter into any agreement which gives him less than some utility level. This commitment is perfectly binding initially. However, once so much time has passed that even receiving the entire pie would yield less than the committed level of utility, then the commitment becomes void. Intuitively, this simply means that no player can remain committed to something which has become impossible. We use a slight refinement of subgame-perfect equilibrium as a solution concept. If only one player can commit, then we find an immediate and efficient agreement on a division which gives the committed player (strictly) between one half and the entire pie, the exact allocation being determined uniquely by the recognition probabilities. If both players can commit sequentially before the bargaining starts, we find a unique equilibrium division with a first–mover advantage. Finally, we consider a version of the game where both players commit simultaneously before the bargaining starts. In this case, there is a range of equilibrium divisions. However, in the limit as the discount factor goes to one, no player obtains less than one third of the pie, even with arbitrarily small proposal power. Somewhat surprisingly, the equal split emerges as the only division supported by an equilibrium for any choice of the discount factor and the recognition probabilities.