[Paleopsych] Economist: (Schelling and Aumann) Economics focus: War games

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Economics focus: War games
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    Oct 13th 2005

    A big pay-off for two game theorists

    THIS year's Nobel prize for economics might almost have doubled as the
    prize for peace. On October 10th, three days after the International
    Atomic Energy Agency and its director-general, Mohamed ElBaradei, won
    their laurels for monitoring the misuse of nuclear power, the
    economics prize was bestowed on two scholars whose best work was also
    done in the shadow of the mushroom cloud.

    Robert Aumann, of Hebrew University, and Thomas Schelling, of the
    University of Maryland, are both game theorists. Game theory is now
    part of every economist's toolkit and has been recognised by the Nobel
    award before, when John Harsanyi, John Nash and Reinhard Selten shared
    the honour in 1994. It is the study of what happens when the
    calculating, self-interested protagonist of economic fable meets
    another member of his kind. In such encounters, neither party can
    decide what to do without taking into account the actions of the
    other.

    During the cold war, two protagonists that captured game theorists'
    imaginations were the United States and the Soviet Union. How each of
    these nuclear adversaries might successfully deter the other was the
    most pressing question hanging over Mr Schelling's classic work, "The
    Strategy of Conflict", published in 1960. The book ranged freely and
    widely in search of an answer, finding inspiration in gun duels in the
    Old West, a child's game of brinkmanship with its parents, or the
    safety precautions of ancient despots, who made a habit of drinking
    from the same cup as any rival who might want to poison them.

    Mr Schelling's back-of-the-envelope logic reached many striking
    conclusions that appeared obvious only after he had made them clear.
    He argued that a country's best safeguard against nuclear war was to
    protect its weapons, not its people. A country that thinks it can
    withstand a nuclear war is more likely to start one. Better to show
    your enemy you can hit back after a strike, than to show him you can
    survive one. Mr Schelling invested his hopes for peace not in arms
    reductions or fall-out shelters but in preserving the ability to
    retaliate, for example by putting missiles into submarines.

    All-out thermonuclear warfare is the kind of game you get to play only
    once. Other games, however, are replayed again and again. It is these
    that fascinate Mr Aumann. In a repeated encounter, one player can
    always punish the other for something he did in the past. The prospect
    of vengeful retaliation, Mr Aumann showed, opens up many opportunities
    for amicable co-operation. One player will collaborate with another
    only because he knows that if he is cheated today, he can punish the
    cheat tomorrow.

    Mutually assured co-operation

    According to this view, co-operation need not rely on goodwill, good
    faith, or an outside referee. It can emerge out of nothing more than
    the cold calculation of self-interest. This is in many ways a hopeful
    result: opportunists can hold each other in check. Mr Aumann named
    this insight the "folk theorem" (like many folk songs, the theorem has
    no original author, though many have embellished it). In 1959, he
    generalised it to games between many players, some of whom might gang
    up on the rest.

    Mr Aumann is loyal to a method--game theory--not to the subject matter
    of economics per se. His primary affiliation is to his university's
    delightfully named Centre for Rationality, not its economics
    department. Trained as a mathematician, he started out as a
    purist--pursuing maths for maths' sake--but soon found his work
    pressed into practical use. Between 1965 and 1968, for example, he
    co-wrote a series of reports for the United States Arms Control and
    Disarmament Agency. The Russians and Americans were pursuing gradual,
    step-by-step disarmament. But the military capabilities of each
    superpower were so shrouded in mystery that neither side knew
    precisely what game they were playing: they did not know what their
    opponents were prepared to sacrifice, nor what they themselves stood
    to gain. Without knowing how many missiles the Russians had, for
    example, the Americans could not know whether an agreement to scrap
    100 of them was meaningful or not.

    In such games, Mr Aumann pointed out, how a player acts can reveal
    what he knows. If Russia were quick to agree to cut 100 missiles, it
    might suggest its missile stocks were larger than the Americans had
    guessed. Or perhaps the Russians just wanted the Americans to think
    that. Examples of such deception are not limited to the cold war. Some
    have speculated that Saddam Hussein pursued a similar strategy in the
    run-up to the invasion of Iraq in 2003. Despite apparently having no
    actual weapons of mass destruction left, he offered only the most
    grudging co-operation to weapons inspectors. The Iraqi dictator
    perhaps wanted to conceal the humiliating fact that he had nothing
    much to hide.

    Messrs Aumann and Schelling have never worked together, perhaps
    because the division of labour between them is so clear. Mr Aumann is
    happiest proving theorems; Mr Schelling delights in applying them. Mr
    Aumann operates at the highest levels of abstraction, where the air is
    thin but the views are panoramic. Mr Schelling tills the lower-lying
    valleys, discovering the most fertile fields of application and
    plucking the juiciest examples.

    In one of his more unusual papers, Mr Aumann uses game theory to shed
    light on an obscure passage in the Talmud, which explains how to
    divide an asset, such as a fine garment, between competing claimants.
    You should give three-quarters to the person who claims all of it, and
    the remaining quarter to the person who claims half of it, the text
    instructs, somewhat inscrutably. Fortunately, the Nobel committee had
    no need for such a complicated rule in dividing up its prize. Between
    its two equally deserving laureates, it split the SKr10m ($1.3m)
    fifty-fifty.