A number of explanations have been proposed for the great boom and bust, most of which focus on greed, overconfidence, and downright stupidity on the part of mortgage lenders, investment bankers, and Wall Street C.E.O.s. According to a common narrative, we have lived through a textbook instance of the madness of crowds. If this were all there was to it, we could rest more comfortably: greed can be controlled, with some difficulty, admittedly; overconfidence gets punctured; even stupid people can be educated. Unfortunately, the real causes of the crisis are much scarier and less amenable to reform: they have to do with the inner logic of an economy like ours. The root problem is what might be termed "rational irrationality"--behavior that, on the individual level, is perfectly reasonable but that, when aggregated in the marketplace, produces calamity.
But society can't afford it when 1 million other families make the same choice. In Finland, it would require the output of a dedicated nuclear reactor.
Or the same idea can be applied to litter. One wrapper dropped in the street is not a problem. Thousands are.
Sam Loyd (1841 - 1911), the American puzzler and 'recreational mathematician' has a rather un-PC visual puzzle called the 'Vanishing Chinaman.' 12 chinamen are printed around the edge of a double dial, with one dial slightly large than the other. The figures are half on the inner dial and partly on the outer dial. But rotating the dial causes the 'appearance' of a thirteenth chinaman.
i.e. how fractional amounts become a problem when multiplied ;-) You can't be me, I'm taken
The idea behind superrationality is that two logical thinkers analyzing the same problem will come up with the same, correct, answer. For example, if two persons are both good at arithmetic, and both have been given the same complicated sum to do, it can be predicted that both will get the same answer before the sum is known. In arithmetic, knowing that the two answers are going to be the same doesn't change the value of the sum, but in game theory, knowing that the answer will be the same might change the answer itself.
Superrationality is an alternative way to reason. First, it is assumed that the answer to a symmetric problem will be the same for all the superrational players. Thus the sameness is taken into account before knowing what the strategy will be. The strategy is found by maximizing the payoff to each player, assuming that they all use the same strategy. Since the superrational player knows that the other superrational player will do the same thing, whatever that might be, there are only two choices for two superrational players. Both will cooperate or both will defect depending on the value of the superrational answer. Thus the two superrational players will both cooperate, since this answer maximizes their payoff. Two superrational players playing this game will each walk away with $100. Note that a superrational player playing against a game-theoretic rational player will defect, since the strategy only assumes that the superrational players will agree. A superrational player playing against a player of uncertain superrationality will sometimes defect and sometimes cooperate.
Note that a superrational player playing against a game-theoretic rational player will defect, since the strategy only assumes that the superrational players will agree. A superrational player playing against a player of uncertain superrationality will sometimes defect and sometimes cooperate.
One example discussed by Hofstadter is the platonia dilemma: an eccentric trillionaire contacts 20 people, and tells them that if one and only one of them sends him a telegram (assumed to cost nothing) by noon the next day, that person will receive a billion dollars. If he receives more than one telegram, or none at all, no one will get any money, and cooperation between players is forbidden. In this situation, the superrational thing to do (if it is known that all 20 are superrational) is to send a telegram with probability p=1/20, which maximizes the probability that exactly one telegram is received. Notice though that this is not the solution in a conventional game-theoretical analysis. Twenty game-theoretically rational players would each send in a telegram and therefore receive nothing. This is because sending the telegram is the dominant strategy; if an individual player sends a telegram he has a chance of receiving money, but if he sends no telegram he cannot get anything.
Notice though that this is not the solution in a conventional game-theoretical analysis. Twenty game-theoretically rational players would each send in a telegram and therefore receive nothing. This is because sending the telegram is the dominant strategy; if an individual player sends a telegram he has a chance of receiving money, but if he sends no telegram he cannot get anything.
With a superrational strategy, people only invest a fraction of their available wealth, such that if everyone invests the same fraction they don't go bankrupt. The "rational" strategy for each individual can well be to invest more, even with leverage, in order to capture more for themselves. En un viejo país ineficiente, algo así como España entre dos guerras civiles, poseer una casa y poca hacienda y memoria ninguna. -- Gil de Biedma
Chuk Prince (The Citi CEO) said it best: "as long as the music plays, we have to dance" What amazed me most in 2006-07 was the number of bankers that were expecting a crash, even hoping to benefit from it (and thus were planning to do exactly that) but yet were still playing the games according to the rules of the over-inflate bubble they knew they were in ("covenant-lite" loans, "pik" (payment in kind) loans, extreme leverage, rockbottom pricing of risk).
What amazed me most in 2006-07 was the number of bankers that were expecting a crash, even hoping to benefit from it (and thus were planning to do exactly that) but yet were still playing the games according to the rules of the over-inflate bubble they knew they were in ("covenant-lite" loans, "pik" (payment in kind) loans, extreme leverage, rockbottom pricing of risk).
- Jake If you only spend 20 minutes of the rest of your life on economics, go spend them here.
