Sunday, October 14, 2012



It’s more than game or a roll of the dice.



At first, it was nothing more than a game. Board games, like chess and backgammon, which have been around for centuries, were simply for fun. Even when card and dice games lured professional gamblers, most people still played for leisure.  Then came professional sports, and games became big business. Nonetheless, it was all part of the entertainment industry. But one day the game left the living room and the baseball field and entered into the research labs of mathematicians and theoretical economists. 

Game Theory” had been largely unnoticed until one of the most brilliant minds of the 20th century, John von Neumann, realized that the mathematical models used in economics did not mirror the way decisions are made in the real world. Rational choice is not simply a matter of weighing alternatives. Reactions and decisions by other people must also be taken into account. Example: the Prisoner's Dilemma.

Imagine two people in jail. While there is insufficient evidence to convict them on a serious charge; there is enough for a lesser offence. The police therefore separate the two prisoners and make each the following proposal: If you testify against the other, you will go free, and he will be imprisoned for ten years. If he testifies and you stay silent, you will receive ten years, and he will go free. If you both squeal, it’s five years each. If you both stay silent, you will each be convicted of the lesser charge and face a one year sentence.

The paradox is that while the best outcome would be for both to remain silent, neither will opt for this strategy. Since each is unable to know if the other is ‘dealing’, they cannot take the risk of staying silent. The Prisoner's Dilemma is remarkable because it shows that two people, both acting rationally, will produce a result that is bad for both of them.

Yisroel Robert. J. Aumann, the Israeli mathematician who attended the Rabbi Jacob Joseph Yeshiva in New York, won the 2005 Nobel Prize in Economics for his work in “conflict and cooperation through game theory analysis.”  In 1985, Aumann demonstrated that Game Theory has its origins in the Talmud (Kesubos 93a) that discusses dividing a late husband’s estate amongst his three wives. (Note: This particular Mishna has puzzled Talmudic scholars for two millennia.)

In short, Game Theory argues (quite convincingly) that individuals acting in self-interest do not always produce positive results. In fact, the opposite is true. When people learn to cooperate, instead of compete, it is advantageous to all parties. But, as the Prisoner's Dilemma suggested, only after repeated encounters would all concerned realize this. Thus, in the late 1970s a competition was announced to find a computer program that generated the most beneficial outcomes, in which the same opponents indeed met repeatedly.

The winning program was devised by another Jew, Anatole Rapoport, who conducted and composed music in Vienna. However, due to the rise of Nazism, he fled to America and mathematical theory. His winning entry called Tit-for-Tat was simple: it began by cooperating, and then repeated the last move of its opponent. It worked on the rule of, “What you did to me, I will do to you,” or “measure for measure.” According to Peace Magazine, the program “punished the other player for selfish behavior and rewarded for cooperation…This proved exceptionally effective, quickly showing the other side the advantages of cooperating. It also set moral philosophers to proposing this as a workable principle to use in real life interactions.” (No Joke: His children reported that he was a bad poker player. Any surprise there?)

Can there be such a thing as an objective/scientific basis for morality? For some, the idea seems absurd. Morality is relative. Moral judgments are not truths, but choices. Indeed, this was the accepted wisdom in philosophy for over a century after Nietzsche had argued for the abandonment of morality, which (parenthetically) he saw as the product of Judaism.

But as Game Theory makes clear the moral principle of measure for measure (in Hebrew, middah k’neged middah) actually works. This axiom can actually be traced back all the way back to the Bible itself.  At the covenant G-d made with Noah, He declared, “Whoever sheds the blood of man; by man shall his blood be shed.” This is simply retributive justice: Tit-for-Tat. In fact, at this point the Torah does something very subtle. The six Hebrew words are a mirror image of one another: [1] Who sheds [2] the blood [3] of man, [3] by man [2] shall his blood [1] be shed. Here, style reflects substance.

The ‘Game’ has a sequel. In 1989, another program, called Generous, beat Tit-for-Tat. It overcame one weakness; a particularly nasty opponent is likely to draw one into a potentially endless and destructive cycle of retaliation, which is bad for both sides. Generous avoided this by randomly but periodically forgetting the last move of its opponent, thus allowing the relationship to begin again. What the programmer named Generous, the Torah refers to as Forgiveness.

Once again, there is a connection to Noah. After the Flood, G-d vowed, “Although the imagination of man's heart is evil from his youth; I will not destroy every living thing as I have done.” This is the principle of Divine forgiveness.

Morality is no longer just a ‘nice’ idea; science and reason demand that we make it a part of our life.  In one of the early works of Jewish philosophy, Sefer Emunos v’Deos (The Book of Beliefs and Opinions), Rav Saadia Gaon (882-942 C.E.) explained that the truths of the Torah could be established by reason. Why then was revelation necessary? Because it takes humanity time to arrive at truth, and there are many slips and pitfalls along the way. Therefore, long before the first game came along, G-d revealed various moral truths that are the basis of His covenant with man: cooperation is as necessary as competition, that cooperation depends on trust, that trust begets justice, and that justice is incomplete without forgiveness.

Darwin preached Survival of the Fittest. Morality guarantees Survival for the long(est) run.

No comments:

Post a Comment