When Solomon became wise for suggesting a baby be split in two to settle a dispute, was he in fact just lucky?
"Lucky", say Avinash Dixit and Barry Nalebuff, the two jovial American business school gurus who have written the "Game Theorist's Guide to Success in Business and Life". The fake mother should have anticipated Solomon's trap. She should have protested as strongly as the real mother. With both women claiming to prefer a living child given to her rival to a dead child shared, his judgement should not have worked as a truth-extracting mechanism.
Dixit and Nalebuff go on to describe "the simplest of the devices that would have worked." Get ready for it. Solomon should announce that he will levy a substantial fine on whoever does not end up with the baby (if all goes well, the fake mother). The first woman is asked to either admit the baby is not hers or claim it is. The second woman is then offered the chance to challenge the claim and make a (monetary) bid for the baby or admit she is faking it. The first woman is offered the chance to concede, but she will have to pay a fine for lying, or to match the bid, in which case the rival pays the fine. It might take you a moment to think it through, but as long as the true mother is prepared to pay more than the false mother would ever be prepared to pay, then this scheme ensures that the first woman tells the truth in the first stage; the second woman tells the truth in the second stage and that no money ever has to change hands.
That, in Dixit and Nalebuff's book, would be the simplest proof of Solomon's sagacity. (Better still if he had generalised it to many women, many babies, repetitions, risk of slight malfunction and any number of other subtleties that fill the publication lists of academic economists ...).
I'll stick to history's judgement that Solomon was wise. He was a judge of character. He sized up the pair, and understood the simple women before him. He played a trick that worked in the circumstances. Indeed, if he had attended one of Dixit's or Nalebuff's business school game theory classes ("the most popular courses at Princeton and Yale," we are told), I think he would have flunked his historical opportunity to become the bye-word for good judgement. Solomon would instead have become the name for the King who loved his own cleverness, who baffled through counter-intuitive complexity and a penchant for paradox.
I co-founded the game theory consultancy company that shot to prominence by designing the auction for 3G spectrum that gave Gordon Brown a £25 billion windfall in 2001--and that was blamed by many for sinking the telecoms industry into a recession from which it has not really recovered. I did my PhD under one of the field's leading figures. I also once believed that Game Theory was the Way and the Truth.
But I have faith no more, and it wasn't just the plain absurdity of examples like Solomon's. Game theory was first developed by polymath Austrian John von Neumann and he elaborated the theory during the WW2 to help with tactical decisions. Since the North Atlantic sea route was the shortest, the German U-boat planners would know that it would be favoured by the Allies; so they would concentrate U-Boats on the Northern crossing; but the Allies, knowing this, would adopt the Southern route to avoid losses; but the Germans, knowing this, would deploy the U-boats to the Southern route ...and therefore the allies could safely use the Northern route. von Neumann developed a theory of tactics that showed us the way out of these circles. He showed that it was important to flip a coin to determine which route would be taken, and that the probabilities should be skewed to the pay-offs. It was a great and useful piece of mathematics. John Nash, the unfortunate schizophrenic anti-hero of ``A Beautiful Mind" showed that the insights of von Neumann can be expanded beyond situations of all-out war.
Application to commerce, where my profits depend on my rivals' behaviour, seems as natural an extension of game theory as business is a peaceful extension of war. But as a Game Theorist who went into business, I can attest that the tactics that Game Theory is good on are almost never critical. By some great piece of PR, Game Theory makes a claim to being the study of Strategy. But that is a pretence. Strategy consultants, for example, are people who try to understand businesses and markets from the inside. What drives the consumer? what is happening to technology? what are the characters and histories of the firms involved? what are the networks of influence. Why do we stop going to Starbucks? What influence does this have on the ecology of high streets? what can Starbucks do now? Will it go bust? Game theory does not answer these sorts of questions of strategy. Once your business judgement is made and your strategic goals are set, then you might pick the brains of one of those Yale MBAs who went to Nalebuff's course for tactical advice.
Even then, you should take any advice with the great pinch of salt that comes with Game Theory's terrible secret: the strongest prediction that it makes is that almost anything is possible in games that are repeated indefinitely. Take any ``Game theorist's guide to life" like this one, look up "Repeated Prisoners Dilemmas" in the index and discover how the author comes clean with the disturbing conclusion that it has no predictive value. Nalebuff and Dixit talk about "Tit-for-Tat", the rule of thumb that says that you should start out repeated interactions by being nice and from then on do as you are done by. If everyone follows this rule, the best collective outcomes are achieved. David Willets, the brainy Shadow Secretary of State for Innovation, Universities & Skills, has spoken lyrically on the Today program of the way that vampire bats are tit-for-tatting when they share blood, and suggested that this provides a philosophical basis for small government, local-community, compassionate Conservatism.
Quite apart from the associations that vampirism has for most voters, Willets should stay off the game theory. Tit-for-Tat is clearly not a good description of the world -- cycles of violence, war and revenge; group loyalties and hierarchies; coalitions of the strong ganging up on the weak ... these common facts of life are quite incompatible with Tit-for-Tat, in which everyone starts nicely, and you are never nastier than anyone has been to you. Nalebuff and Dixit's evasion strategy is to move from claiming they have a description and prediction of the world to hoping they have a prescription for the world. If your theory doesn't fit the world, try changing the reality. After all, this is a "Guide to Success" we are being offered.
Unfortunately, game theory has probably been quite successful at doing this, certainly amongst the MBAs who have been moving from the classroom to Wall Street. Game theory, I think, encourages the following four habits: 1) to look to extract maximum advantage from the rules you are subject to 2) to concentrate on the minutiae of play rather than think about your place in the wider constellation of the business world and society, 3) to always have foremost in your mind: ``what is the payoff?'' and 4) to treat most situations in life as limited and cut-off from all others. The relationship between these four habits and the financial crisis are pretty obvious: stretch every rule to its limits; don't worry about system-wide effects; ignore any general thoughts about the value of living a good life and measure success in the number of Ferraris you can afford. Game theory has, in a way, made a part of the world in its image--the world of finance--and we are now trying to rescue ourselves form it.
So where does this leave our ``Guide to success in Business and in Life''? Probably not as a must read unless you want to go into a few of the areas where Game Theory really has been useful -- competition law, running complicated auctions (usualy for the public sector or a monopolist like Google), utility regulation and military micro-tactics. And what about as a guide to life? The greatest blind-spot in Game Theory here is that the games you play and the way you play them change you as a person. Today's game and tactic changes the games and payoffs you will face tomorrow. Just as micro-planning does not work in the macro-economy, so life-planning cannot be built up from situational tactics. Squeezing out responsible politics from the economy is like trying to lead a good life without ethics.
The financial crisis is a crisis for economics too: why did the discipline fail to notice such a disaster on its watch? worse, has it contributed to the world that made the disaster possible? My prediction is that Game Theory and other studies in economic minutiae are going to loose their shine. Economic history and macro-economics will come out of the crisis well. But books like this will seem so pre-lapserian.
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