Optimal Opacity in Ultimatum Offer Bargaining
We consider a responder whose willingness to pay in an ultimatum bargaining game is common knowledge. Can the responder gain from delegating decision making to a player with opaque preferences? We show that the responder can benefit from such opacity, even if his delegate's expected willingness to pay equals the known willingness to pay of the responder. We determine the optimal shape of opacity and discuss comparative static properties. We also study the robustness of the results with respect to risk aversion and to the offer maker's ability to also resort to a delegate with an opaque offer-making rule. The optimal opacity choice implements efficiency and provides both negotiation parties a positive rent.