by Prof. Yisrael Aumann
Two men — let us call them Reuben and Simon — 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."
Reuben is a rational person and realizes the golden opportunity that has fallen his way. He turns to Simon with the obvious suggestion: "You take half and I'll take half, that way each of us will have $50,000."
To his surprise, Simon 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."
Reuben can hardly believe his ears. What has happened to Simon he asks himself. Why should he get 90% of the money and I just 10%? He decides to try to convince Simon 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."
Simon, however, doesn't seem perturbed by his friend's logic He listens attentively, but when Reuben is finished he says, even more emphatically than before: "90-10 or nothing. That is my last offer."
Reuben's face turns red with anger. He is about to punch Simon in the nose, but he steps back. He realizes that Simon 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 Simon's hand and leaves the room humiliated.
This case is called 'The Blackmailer's Paradox" in game theory. The paradox is that Reuben 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 Simon is sure of himself and doesn't flinch when making his exorbitant demand. This convinces Reuben that he must give in so as to make the best of the situation.
The Arab-Israeli Conflict:
The relationship between Israel and the Arab countries is conducted along the lines of this paradox. At each stage of negotiation, the Arabs present impossible, unacceptable starting positions. They act sure of themselves and as if they totally believe in what they are asking for, and make it clear to Israel that there is no chance of their backing down.
Invariably, Israel agrees to their blackmailing demands because otherwise she will leave the room empty handed. The most blatant example of this is the negotiations with Syria that have been taking place with different levels of negotiators for years. The Syrians made sure that it was clear from the beginning that they would not compromise on one millimeter of the Golan Heights.
The Israeli side, eager to have a peace agreement with Syria, internalized the Syrian position so well, that the Israeli public is sure that the starting point for future negotiations with Syria has to include complete withdrawal from the Golan Heights, this despite its critical strategic importance in ensuring secure borders for Israel.
The Losing Solution:
According to game theory, Israel has to change certain basic perceptions in order to improve her chances in the negotiations game with the Arabs and win the long term political struggle:
a. Willingness to forego agreements:
Israel's political stand is based on the principle that agreements must be reached with the Arabs at any price, that the lack of agreements is untenable. In the Blackmailer's Paradox, Reuben's behavior is the result of his feeling that he must leave the room with some money, no matter how little. Because Reuben cannot imagine himself leaving the room with empty hands, he is easy prey for Simon, and ends up leaving with a certain amount of money, but in the role of the humiliated loser. This is similar to the way Israel handles negotiations, her mental state making her unable to reject suggestions that do not advance her interests.
b. 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. Reuben saw his problem as a onetime event, and behaved accordingly. Had he told Simon 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 Simon, the latter would remember Reuben's original suggestion and would try to reach a compromise.
That is how Israel has to behave, looking at the long term in order to improve her position in future negotiations, even if it means continuing a state of war and fore going an agreement.
c. Faith in your opinions
Another element that creates the "Blackmailer's Paradox" is the unwavering belief of one side in its opinion. Simon 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. Several years ago, I spoke to a senior officer who claimed that Israel must withdraw from the Golan Heights in the framework of a peace treaty, because the Golan is holy land to the Syrians and they will never give it up. I explained to him that first the Syrians convinced themselves that the Golan is holy land to them, and then proceeded to convince you as well. The Syrians' unflinching belief that they are in the right convinces us to give in to their dictates. The only solution to that is for us to believe unwaveringly in the righteousness of our cause. Only complete faith in our demands can succeed in convincing our Syrian opponent to take our opinion into account.
As in all of science, game theory does not take sides in moral and value judgments. It analyzes strategically the behavior of opposing sides in a game they play against one another. The State of Israel is in the midst of one such game opposite its enemies. As in every game, the Arab-Israeli game involves interests that create the framework of the game and its rules.
Sadly, Israel ignores the basic principles of game theory. If Israel would be wise enough to behave according to those principles, her political status and de facto, her security status, would improve substantially. ?
Eiditor's Note: Some of the readers' comments point out other considerations.
1. Dr.Auman's Analysis ?I respectfully disagree with at least part of Dr. Auman's analysis because of a simple reason. In his model, both Reuben and Simon want to walk away with money; Simon is merely trying to maximize his return by playing on the insecurities of Reuben (through the blackmail). So the theory is if Simon presses his position strong enough, he'll walk away with more. But our Arab cousins are not interested in any solution that doesn't totally destroy Reuben even if it leaves him with nothing! (c.f. suicide bombing) ?em, brooklyn (07/06/10)
2. Prof. Aumann left out one big important factor! ?As Arafat himself pointed out after the Clinton administration attempt at "Lets Help Israel and the Pals Negotiate:" The most strategic game the Pals are playing is the game they play with with their own people. Arafat told Clinton: " If I go back with what you offered, my own people will lynch me and find a new leader! " ?hiddenheard, (07/06/10)
3. A different game is played ?1. The $100,000 money that is offered for negotiations was originally robbed from Reuben and rightfully belongs to him. ?2. Simon is paid billions on the side to encourage him to negotiate. If he ends the game he will lose those billions. So it's in his interest to continue the game indefinitely. ?3. It is not the case that the $100k is in the suitcase. It is actually in Reuben's bank account. The game consists of convincing Reuben to make a "unilateral (cash) withdrawal " and hand the money to over to Simon, who will use the money to finance his robbery operations against Reuben. ?Eliezer, Brooklyn (07/06/10)
4. Blackmail ?The present situation only continues because of the prevalence of Jew-hatred in the world. Egypt and Jordan have accepted massive aide packages for peace. So they fight a war by proxy using the "palestinians ". It works beautifully, by remaining "stateless " these people do not have to abide by any laws, and there are enough splinter factions that if one is appeased another can make new demands. We go along with the charade hoping that someday things will improve. When will anyone ever point out that the emperor is naked? Israel WON a defensive war against Egypt and Jordan. "displaced " citizens of those countries should be under their control. Arabs that choose to leave Israel fall into that category, as well as any who can not pledge an oath of loyalty. It should be up to Egypt and Jordan to control them, and or give them a state. Pure and simple. ?bb, Karmiel (07/06/10)
5. Tactical Changes ?Logic and reason are not of any value in this type of negotiation. Morality and common sense mean nothing either. The best example of a well-prepared player in this game is a professional gambler. Frankly, the stakes are too high to allow anyone else. Probably a poker genius with years of experience in high-risk games would react best under intolerable pressure, and could pull off more than one victory with ease. Faith is also a critical factor, so a person whose beliefs are rock-solid is essential. Perhaps Mr. Netanyahu could employ an adviser with those traits, e.g., an orthodox Rabbi who makes a living at the casinos in Nevada.... shrewd, supremely confident, lucky and with a friend in the highest of all places. ?Dorian, Sparks (07/06/10)
Yisrael Aumann is a professor at the Center for the Study of Rationality in the Hebrew University of Jerusalem in Israel. He also holds a visiting position at Stony Brook University and is one of the founding members of the Center for Game Theory in Economics at Stony Brook. Aumann received a Nobel award in Economics in 2005 for his work on conflict and cooperation through game-theory analysis.
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