Israel’s Conflict as Game Theory

By Prof. Yisrael Aumann
Nobel Prize Laureate

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 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, Rick’s behavior 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. 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.

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.

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 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.

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.

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Copyright Yisrael Aumann

20 Responses to “Israel’s Conflict as Game Theory”

  1. lakshmi Says:

    Excellent article, you nailed it on Israel. And I appreciate the example of game theory-it is instructive whenever two people(s) enter into some dispute and negotiation.

  2. Paul Kersey Says:

    Yes, this seems to describe Reagan and Thatchers’ strategy against the Soviet Union, as well. Isn’t this similar to something called Brinkmanship?

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  4. Barrett Kalellis Says:

    Seems only like common sense — belief in the rightness of one’s own opinions. It’s too bad that most politicians are unable to stand on principle and continually look for the chimera of compromise.

  5. einat Says:

    The problem is that Israel BELIEF IN THE RIGHTNESS OF HER OPINION in the need of peace at any cost. Because of this view the people leeding it convince themself of the less value of other issues and since they have to convince the Israely public they invent all kind of unrealistic arguments and excuses which by themself increase their trust on their way.

  6. ObamaYoMoma Says:

    If Israel would be wise enough to behave according to those principles, her political status and de facto, her security status, would improve substantially.

    Perhaps if this was only a conflict between Arabs and Israelis as the writer naively defines it, but it’s not, it is a jihad of conquest being waged against Israel by Dar al Islam, and like all jihads being waged by Dar al Islam against infidels it is permanent. Hence, no peace is possible. Indeed, no matter how suicidal the concessions that Israel caves into, all it will do is further embolden Dar al Islam. That’s the problem: Israelis don’t want to accept the reality that the jihad being waged against it is permanent.

  7. Danny Says:

    Obama you are exactly right. I wish the world would understand this simple fact

  8. AntiOnan Says:

    What is rather appropriate, is that you can extend the “game” allusion even further to the fact that, like in many sports, it isn’t the aggressor who is punished, but the victim who finally decides to retaliate after no little provocation.

  9. Ralgood Says:

    Something in this bothers me. If, as Mr. Aumann writes:

    “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. “

    why would Israel give up the Golan Heights if doing so no longer provides it with secure borders????

  10. jock Says:

    Ralgood,

    You are quite right and indeed Aumann is making your point too. Jock

  11. Andrew Says:

    So, The Suitcase with $100k is the equivalent of the Golan and the occupied Palestinian Lands? 50:50 you suggest is rational? So to you Rick is potentially Israel if it does not change its behavior, would otherwise lose 90% of the lands it occupies to Steve’s equiavalent: the Palestinians and Syria?

    Is this quality of reasoning the Noble Prize Kind or has your Jewish Zeal taken the best of your analysis?

  12. pathfinder58 Says:

    First, I must comment that Prof. Aumann’s comparison between border negotiations and game theory is breathtaking in its simplicity and lucidity. Thank you professor!

    Any woman negotiating a deal on a knock-off designer purse at a state fair understands this principle. You can never get a fair deal, unless you walk away… The western world needs to support and trust Isreal, even if they must walk away from the negotiating table with nothing.

  13. Wm Hausman Says:

    Obamayomoma is correct and he has the history of dar al-Islam to substantiate his assertion, i.e., that the Islamic mindset is so rigidly impassioned with its rightness, it is hopelessly irrational. And they have 1400 years of un-wavering conviction, similar to the psychotic who will not give up his delusions regardless of overwhelming contrary evidence presented to him. But there’s another complicating factor here and that is Mr. Obama. No amount of contrary evidence, no amount of advice, and no amount of warning will dissuade him from trying castrate Israel (except maybe a significantly changed House of Representatives). Louis Farrankhan of Nations of Islam, and Jeremiah Wright are long time intimates and the second highest visitors to the White House. Enough said.

  14. AntiOnan Says:

    If Israel’s leaders does NOT change their attitude and realise that there can never be a peace while Israel exists and probably while there is still one Jew left alive, then it will cease to exist, as they do NOT and never have, wanted peace. They only want the destruction of Israel.

    Islam has had 1400 yrs, or so, of polishing its rhetoric, its strategy & its tactics (most of which were practised by more recent totalitarian states in Germany & Russia) and these have never changed since Muhammad died. While the majority sects of Islam still push for barbaric Sharia law implementation, Israel stands out as a beacon and the symbol of western virtue. While the Arabs have done nothing to alleviate the suffering of their own peoples, Israel turned deserts into orchards while threatened on all sides.

    If Israel perishes so will the west and mankind’s greatest creation: the western state which despite its innate faults still feeds and subsidises much of the world

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  16. Yiftach Says:

    @Andrew: No, no, and no. This isn’t a literal comparison, it’s a METAPHOR. I’m not sure if reading the piece again will help you, but please go ahead and read it again, and try to fathom the underpinnings of game theory and how Prof. Aumann very deftly uses them to relate his opinion of the Arab-Israeli conflict.

  17. Citizen Warrior Says:

    ObamaYoMoma, you make an excellent point. I was reading an article by Barry Rubin called A Middle East Strategy for the West, when I read this sentence: “The problem is not just that cynical rulers (in the Middle East) mislead the masses through demagoguery — though that’s true; it’s that the masses embrace extremist world views.”

    I had to do a doubletake. If the masses are embracing it, then it’s not extremist, right? It’s mainstream. By the term, “extremist world views” he is really saying “following classic, mainstream Islamic teachings.” But what a politically-correct, double-talk way of saying it!

    Rubin did say something worthwhile in the article, however. He wrote: “Obtaining Israel-Palestinian or Arab-Israeli peace is a useless strategy, distracting from real issues. It isn’t going to happen; Islamists would use any such peace to portray those signing it as traitors; and even many Arab nationalists would denounce it to raise their credibility as tough, unyielding fighters. Violence and unrest would increase, not lessen, as a result.”

    Absolutely. All this talk of “peace in the Middle East” is ridiculous. It’s not going to happen. EVER! Get over it. Muslims will not ever give up trying to “drive the Jews into the sea,” and the Israelis will not ever give up trying to survive. The world needs to embrace this reality and aim for something actually attainable: An Israeli population that is relatively safe from Jihadis.

    I’m not a Jew, by the way. I don’t have any special attachment to the Jewish religion or Israel, except that it’s a democracy, and by far the best democracy in the Middle East. As Glen Reinsford wrote in his article Understanding the Arab-Israeli Conflict, “Perhaps the greatest of all ironies in the present-day Middle East, as David Horowitz has pointed out, is that Arab Israelis enjoy more social, legal and political freedom than do Arabs in any one of the fifty-three Muslim countries.” Ironic because so many Arabs are hell-bent on destroying Israel.

    But Israel needs to embrace this reality too and quit bending over backwards to “make peace.” They keep being lured into making deals with the ruling Jihadis of the day in order to finally have “peace.” They should be able to look at their own history in the Middle East, or look at easily-obtained Islamic teachings and see that “peace agreements” with Jihadis are worse than a waste of time (for example, Qur’an 9:1-17).

    One particular Islamic principle the Israelis might discover within fifteen minutes of perusing Islamic texts is that no peace agreements between Muslims and non-Muslims can last longer than ten years, and the only Islamic purpose for a peace agreement is to get the enemy to stop attacking Muslims while the Muslims regroup and strengthen their position, allowing them to take up the fight again at a time of their choice from a position of strength.

  18. Conservababe Says:

    Exploring the idea of variables:

    Let’s say that Rick, the rational one, needs the money for medical care for his daughter. And let’s say he is a martial arts expert, while Steve is a 90-lb weakling. That changes things a bit.

    Using that premise, all Rick has to do is say, “This is too important to quibble over. If you’re going to be irrational, I’ll just take the entire $100,000. You tell the man when he asks if we have come to an agreement that the answer is yes.”

    Two things change the outcome of the argument in favor of the rational, rather than the irrational player: The absolute necessity to win and the willingness to use force that the other doesn’t have in order to control the outcome.

    Israel, in the battle for its existence, has had the will in the past to use force to “control the argument.” The problem now is, Israel (and the U.S. in its proxy wars with Syria, Iran, Russa, etc.) might as well not have the strong militaries (the “marial arts training”) they possess because they are too afraid of world opinion or sanctions to use them.

    Now maybe Rick is afraid that the man running the argument will see him as a bully and not see this as a genuine “agreement.” (Just as Israel — and the U.S. — face the world calling them imperialist war-mongers, unwilling to negotiate).

    How important is the child’s life to Rick? If she’s dying, he will take the risk of being seen as a bully or worse. Likewise, if Israel (and the U.S — and other Western powers) face the fact that “their child” (Western civilization) is dying, they will ignore world opinion and do what they need to do.

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