Weakening the Weak may Harm the Strong. A Bargaining Model where Opting-In is Costly

The opportunity to bargain often causes costs for at least one party in many economic situations, e.g. wage negotiations, joint ventures or interfirm cooperation. This paper studies such situations. A "strong" and a "weak" player have to agree how to divide the produced surplus. The "weak" player has to bear opting in costs. We characterize the set of subgame perfect equilibria. It is shown (i) that raising the costs of the weak party may strictly lower the payoff of the strong party, (ii) that for some cost levels the only equilibrium is inefficient, (iii) that if the players are sufficiently patient the outcomes of the "zero-cost model" and the "vanishing costs" version of our model do not coincide, and (iv) that in general multiplicity of equilibria arises.