Strategic ignorance in ultimatum bargaining

•We analyze Schelling's conjecture that ignorance might be strength.•Proposers who are kept ignorant almost always realize their most preferred option.•Using ignorance strategically pays if opponents are uncertain about intentions. In his classic article “An Essay on Bargaining” Schelling (1956) argues that ignorance might actually be strength rather than weakness. We test and confirm Schelling's conjecture in a simple take-it-or-leave-it bargaining experiment where the proposer can choose between two possible offers. Option A always gives the proposer a higher payoff than option B. The payoff of the responder depends on the (randomly determined) state of nature. In one state payoffs of the two players are aligned whereas they are not aligned in the other state. The responder is always informed about the actual state. The proposer knows the actual state in our first treatment but not in the second. We find that proposers indeed benefit from ignorance because the responders accept almost all offers (even the unfavorable ones) if the payoffs are not transparent for the proposer. In additional treatments we investigate bargaining situations where the proposer can deliberately remain ignorant.