TWO MEN - let us call them Rick and Steve - are put in a small room containing a suitcase filled with bills totaling $100,000. The owner of the suitcase announces the following:"I will give you the money in the suitcase 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." Rick is a rational person and realizes the golden opportunity that has fallen his way. He turns to Steve with the obvious suggestion: "You take half and I'll take half that way each of us will have $50,000." To his surprise, Steve 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". Rick can hardly believe his ears. "What has happened to Steve" he asks himself. "Why should he get 90% of the money and I just 10%?" He decides to try to convince Steve 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." Steve, however, doesn't seem perturbed by his friend's logic. He listens attentively, but when Rick is finished he says, even more emphatically than before: "90 - 10 or nothing. That is my last offer." Rick's face turns red with anger. He is about to punch Steve in the nose, but he steps back. He realizes that Steve 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 Steve's hand, and leaves the room humiliated. This case is called 'The Blackmailer's Paradox" in game theory. The paradox is that Rick the rational is forced to behave irrationally by definition, in order to achieve maximum results in the face of the situation that has evolved. What brings about this bizarre outcome is the fact Steve is sure of himself and doesn't flinch when making his exorbitant demand. This convinces Rick that he must give in so as to make the best of the situation
The Losing Solution
In the Blackmailer's Paradox, Rick’s behaviour is the result of his feeling that he must leave the room with some money, no matter how little. Because Rick cannot imagine himself leaving the room with empty hands, he is easy prey for Steve, and ends up leaving with a certain amount of money, but in the role of the humiliated loser.
Taking repetition into account, Game theory relates to onetime situations differently than to situations that repeat themselves. A situation that repeats itself over any length of time, creates, paradoxically, strategic parity that leads to cooperation between the opposing sides. This cooperation occurs when both sides realize that the game is going to repeat itself, and that since they must weigh the influence present moves will have on future games, there is a balancing factor at play. Rick saw his problem as a onetime event, and behaved accordingly. Had he told Steve instead that he would not forego the amount he deserves even if he sustains a total loss, he would have changed the game results for an indefinite period. It is probably true that he would still have left the game empty handed, but at the next meeting with Steve, the latter would remember Rick's original suggestion and would try to reach a compromise.
Faith in your opinions, another element that crates the "Blackmailer's Paradox" is the unwavering belief of one side in its opinion. Steve exemplifies that. This faith gives a contender inner confidence in his cause at the start and eventually convinces his rival as well. The result is that the opposing side wants to reach an agreement, even at the expense of irrational surrender that is considerably distanced from his opening position.
As in all of science, game theory does not take sides, in moral and value judgments. It analyzes strategically the behaviour of opposing sides in a game they play against one another
Prof. Yisrael Aumann, Israel's leading expert and Nobel Prize Laureate on Game Theory as it applies to Conflict as related by Naomi Ragen on October 29, 2010.
Reviewed March 2015