Missing a critical point, as well, are Utopian free marketeers, who imagine that a mere complex of free-trade agreements will bring about a world perfectly pacified by the lures of commerce. Essential to the transition is military power sufficient to defend against any feasible threat. Weakness enhances the rewards of adversaries’ military strength. The kind of disarmament sought in the Peace Now movement invariably leads to war because it renders military strength relatively more rewarding than the saving and sacrifice needed for economic advance. Complete disarmament is the most dangerous condition of all because it offers the maximum reward for secret armament. Thus disarmament is likely to cause the rapid and unpredictable acquisition of weapons and result in imbalances whenever aggression is rewarded. As the U.S. nuclear deterrent deteriorates, for example, the value of the nuclear capabilities in Iran or other hostile countries rises inexorably.
Crucial to successful negotiation is long-term commitment. Irrational behavior may be rational in a game if it conveys an absolute commitment to a goal. An example cited by Aumann is what he brilliantly calls the “blackmailer’s paradox.”
Alice and Bob must divide a thousand dollars. It is not an ultimatum game; they can discuss it freely. Bob says to Alice, “Look, I want nine hundred of those thousand dollars. Take it or leave it. I will not walk out of this room with less than nine hundred dollars.” Alice says, “Come on. That’s crazy. We have a thousand dollars. We should divide it evenly.”
“You may say it’s crazy or not crazy, but I’m not walking out with less than 900.” Bob stands his ground, and since 100 is better than nothing, Alice takes the hundred.
The paradox is that the irrational guy is Bob. He is crazy. But he gets the 900 dollars. It would seem that in a rational game the irrational guy should get less rather than more. The answer to the paradox is that Alice can also declare that she’s not walking out of here with less than 900 dollars. Then it becomes a test of wills and capabilities. The important thing is that the person who is making this demand has to convince the other one that he is absolutely serious.
Bob, when he says 900 dollars, has to convince Alice that he is really serious. He’s crazy, but crazy and serious are not mutually exclusive categories. Alice, likewise — if she doesn’t want to capitulate — has to convince Bob that she, too, is serious. In order to convince the other person, you must first convince yourself. That is another part of the paradox. Conviction is a process of conversion in which identity itself is engaged. Such immovable convictions are often termed religious. In some sense, they transcend reason and partake of the domains of faith. The rational man at some point has to make a religious stand. He makes a commitment by declaring some entity as holy.
All the usual trite objections that game theory is valid only in a world of rational calculators engaged solely by materially calculable goals — economic players — ignore the essential importance of sacred commitments. Focusing on behavior and response, the theory implicitly comprises all motives, including sin and hate, love and worship. If the Palestinians — goaded by more than a century of anti-Semitic propaganda, aggravated by daily gouts of shame and envy — do in truth prefer killing Jews to life itself in a Palestinian nation, then the game will embrace that motive. Israel will ultimately build a fortress, backed by a nuclear deterrent and any additional combination of deadly or defensive technologies. Precisely by taking the Palestinians at their word, the Israelis may cause them to think again. Perhaps life excluded from the wealthy fortress next door will not be so attractive. Perhaps peace would at last seem preferable.
In early December 2008, I traveled to Toronto to hear the 78-year-old Aumann speak. It was a rare experience of the religion of rationality.
Aumann stood at the podium like a prophet, his long, white beard making him look like the Talmudic scholar he is or like a prophet of yore, his hoary voice tinged with hints of Hebrew, all lending a hallowed resonance to his words, which came slowly, one at a time, as if extracted painfully and precariously from an aging brain, still lagging seven hours, or perhaps thirty-six centuries, behind the times of modern Toronto. For Aumann was trying to explain his ardent belief that his Canadian hosts for the evening, celebrating “Israel at Sixty” — and indeed most observers of Israel and its predicament — had gotten it wrong, way wrong, wrong by many orders of magnitude.
As a preeminent living Israeli scientist and leading exponent of mathematical rationality, Aumann is one of the world’s most modern thinkers. Although his prime field is game theory, he is one of the world’s leading mathematicians and economists. But his audience that evening was a crowd of politically conservative Jews gathered in the comfort of the synagogue conference center of Aish HaTorah, meaning “Fire of the Torah.” In the continuing conflict between the times and the Torah lies a revealing dimension of the Israel test. To the fire of the Torah, Aumann brings the ice of reason, but as the audience would learn, there is enormous fire in his ice.
Nervous about Aumann’s initial, halting delivery and long, pregnant silences, some in his audience began shifting in their seats, half fearing that this crusty old scholar might break down. Others worried that he was coming down from his distant mountain in Jerusalem, enflamed with a vision of truth, to deliver an Israel test as a list of mathematical problems. Or that he would unveil a series of stone tablets inscribed with a set of abstruse equations, together with the claim that his listeners must turn from the golden calves of commerce, the Kosher feasts on the groaning boards of this gala event, and the numinous laws of the Torah upheld in this Orthodox synagogue, and bow to the revelation of mathematical logic. But Aumann had something else on his mind that evening. He would explain that his game-theory insights were all of a unity with his monotheistic Judaism. But his first observation was simple, factual, mathematical, and holy.
“Israel,” he said, “is not sixty years old. It is sixty times sixty years old.”
Gathered to celebrate and discuss “the state of our future” in black ties and evening best, the audience was somber. Earlier in the evening Caroline Glick, the eloquent Cassandra of The Jerusalem Post, warned the group over dinner of the portentous meaning of the massacre of Jews a few days before at Mumbai’s Chabad House in India. There jihadist terrorists took time off from an assault on the Taj Mahal Palace Tower hotel and other monumental structures inherited from a long-gone empire to torture and kill a small assemblage of Jews at a nondescript school for orphans nearly a mile away.
“They did it,” she said, “with long advanced planning and with an ecstatic relish of murderous hatred.”
For 24 hours, The New York Times, CNN, and other notable media, as she reminded the audience, ignored the attack on the Chabad House. Then in subsequent days they appeared baffled by this digression in the path of terror, which struck the eminent editors of the Times as “senseless.” They ruminated on the possible strategic significance of the Jewish center as a vantage point for an attack on Mumbai’s more consequential targets, such as military bases or business centers. But Glick readily decoded the message from the bloody rubble and easily read the miasmic minds of the murderers.
“We recognize that wherever we are, the primary target is always us. The essential take-home lesson from Mumbai, the historic lesson from Mumbai, is that we are on our own. Our destiny is in no one’s hands but our own. Our greatest achievements have come when we recognized that we must trust in ourselves. The greatest calamities come when we trust in others to save us….