Unique Inneficient Perfect Equilibrium in a Stochastic Model of Bargaining with Complete Information

We consider a two-player strategic bargaining model with discounting in which (i) the interim disagreement point in each period is stochastically determined at the beginning of the period, and (ii) the proposing player can delay in making an offer. Unlike many other bargaining models of complete information, in which inefficient perfect equilibrium outcomes are caused by the multiplicity of perfect equilibrium outcomes, our model has a unique perfect equilibrium payoff in most of the cases. For some parameter values, the perfect equilibrium is inefficient since it has a stochastically delayed agreement. We show that both (i) and (ii) are also necessary for the unique inefficient equilibrium outcome in our model.