The Blackmailer’s Paradox
Two men, let us call them Alex and Brian, are put in a small room containing a suitcase filled with bills totaling £100,000. The owner of the suitcase tells them:
“I will give you this money under one condition…you have to negotiate an agreement on how to divide it. That is the only way I will agree to give you the money.”
Alex is a rational person and rearises the golden opportunity that has fallen his way. He turns to Brian with the obvious suggestion: “You take half and I’ll take half, that way each of us will have £50,000.”
To his surprise, Brian frowns at him and says, in a tone that leaves no room for doubt: “Look here, I don’t know what your plans are for the money, but I don’t intend to leave this room with less than £90,000. If you accept that, fine. If not, we can both go home without any of the money.”
Alex can hardly believe his ears. “What has happened to Brian” he asks himself. “Why should he get 90% of the money and I just 10%?” He decides to try to convince Brian to accept his view. “Let’s be logical,” he urges him, “We are in the same situation, we both want the money. Let’s divide the money equally and both of us will profit.”
Brian, however, doesn’t seem interested in his friend’s logic. He listens attentively, but when Alex is finished he says, even more emphatically than before: “90-10 or nothing. That is my last offer.”
Alex’s face turns red with anger. He is about to punch Brian in the nose, but he steps back. He realizes that Brian is not going to relent, and that the only way he can leave the room with any money is to give in to him. He straightens his clothes, takes £10,000 from the suitcase, shakes Brian’s hand and leaves the room humiliated.
This case is called ‘The Blackmailer’s Paradox” in game theory. The paradox is that Alex the rational is forced to behave irrationally by definition,