ULTIMATUM BARGAINING

IN Chapter 1, we examined a bargaining game in which the position of the participants was entirely symmetric. Here we move to the other extreme, where one participant has – or appears to have – all the bargaining power. Again, there is a good to be divided if a bargain can be struck. The advantaged party gets to issue an ultimatum: “I want so much; take it or leave it.” The disadvantaged party accepts or not. If it is “yes,” the ultimatum giver gets what she asked for, leaving the rest for her partner. If it is “no,” neither gets anything.

The reasoning for the ultimatum giver’s advantage goes as follows. If the second player is offered a small amount, he will take it, since something is better than nothing. The ultimatum giver can see this, so he asks for almost all the good. Then the second player agrees.

The advantage is that the first player has only one move in the game, which is giving the ultimatum. She is not given any opportunity to revise her demand. She is committed. If the responder were given the opportunity to pre-commit to a minimum acceptable share and make it known before anything happened, then he would be the ultimatum giver, and have the bargaining advantage.

SEQUENTIAL RATIONALITY

In Stanley Kubrick’s 1963 film, Dr. Strangelove, or How I Learned to Stop Worrying and Love the Bomb, the USSR has built a doomsday machine – a device that, when triggered by an enemy attack or when tampered with in any way, will set off a nuclear explosion potent enough to destroy all human life. The doomsday machine is designed to be set off by tampering, not to guard it from the enemy but to guard it from its builders having second thoughts. For surely if there were an attack, it would be better for the USSR to suffer the effects of the attack than to suffer the combined effects of the attack and the doomsday machine. After an attack, if they could, they would disable the doomsday machine. And if their enemies could anticipate this, the doomsday machine would lose its power to deter aggression. For this reason, the commitment to retaliate had been built into the doomsday machine. Deterrence requires that all this be known. There is a memorable scene in the film in which Peter Sellers as Dr. Strangelove shouts: “You fools! A doomsday machine isn’t any good if you don’t tell anyone you have it!”