Sunday, October 04, 2009

Smith and the Prisoner's Dilemma





Gavin Kennedy

John Cassidy writes on: “Rational Irrationality: The Real Reason That Capitalism Is So Crash-Prone” in The New Yorker (5 October). Normxxx comments, parenthetically, on Cassidy’s thoughts in normxxx ruminates... HERE
[[comments in double-square brackets are normxxx’s]]

Because financial markets consist of individuals who react to what others are doing, theories of 'free-market economics' are often less illuminating than the Prisoner's Dilemma, an analysis of strategic behavior that game theorists associated with the RAND Corporation developed during the early nineteen-fifties. Much of the work done at RAND was initially applied to the logic of nuclear warfare, but it has proved extremely useful in understanding another 'explosion-prone' arena: Wall Street.

Imagine that you and another armed man have been arrested and charged with jointly carrying out a robbery. The two of you are being held and questioned separately, with no means of communicating. You know that, if you both confess, each of you will get ten years in jail, whereas if you both deny the crime you will be charged only with the lesser offense of gun possession, which carries a sentence of just three years in jail. The best scenario for you is if you confess and your partner doesn't: you'll be rewarded for your betrayal by being released, and he'll get a sentence of fifteen years. The worst scenario, accordingly, is if you keep quiet and he confesses.

What should you do? The optimal joint result would require the two of you to keep quiet, so that you both got a light sentence, amounting to a combined six years of jail time. Any other strategy means more collective jail time. But you know that you're risking the maximum penalty if you keep quiet, because your partner could seize a chance for freedom and betray you. And you know that your partner is bound to be making the same calculation. Hence, the rational strategy, for both of you, is to confess, and serve ten years in jail. In the language of game theory, confessing is a "dominant strategy," even though it leads to a disastrous outcome. [[What you are trying to do is minimize your maximum possible loss.: normxxx]]

The Prisoner's Dilemma is the obverse of Adam Smith's theory of the invisible hand, in which the free market coordinates the behavior of self-seeking individuals to the benefit of all. Each businessman "intends only his own gain," Smith wrote in "The Wealth of Nations", "and he is in this, as in many other cases, led by an invisible hand to promote [[a socially positive: normxxx]] end which was no part of his intention". But in a market environment the individual pursuit of self-interest, however rational, can give way to collective disaster. The invisible hand becomes a clenched fist

There is a mixture of interesting ideas in this part of John Cassidy’s article, “Rational Irrationality”, in the New Yorker (5 October), on some perspectives of which I would put a different slant.

The two-person, single-round, Prisoner’s Dilemma game illustrates the choice between ‘co-operation’ and ‘defection’. Roughly, does a player independently choose to ‘co-operate’ or ‘defect’ (or, say, choose ‘trade’ or ‘plunder’)? This boils down to ‘doing what is best for self’ or ‘doing what’s best for both of us’.

The original Prisoner’s Dilemma (which is why it was called “prisoner’s dilemma”) is actually a 3-person game, with the detectives imposing the pay-offs of the two prisoners' choices, over which they had a contrary interest (law and order) to that of the criminals (getting away with their crimes).

In ‘co-operation’/’defection’ games the players’ gain or lose according to their choices. If one of them defects and is successful, her individual, positive payoff will be larger than the player who attempts to cooperate and loses, with a negative payoff. If both defect, successive rounds will produce losses for both of them (maximum sentence in prison, in which they can 'explain' to each other why they chose the defection option (confessing) to trap the other in not confessing!

If both cooperate (not confess) and are successful, they both gain a positive payoff, smaller than the gainer from an individual defection, but they have the prospect of repeating rounds of positive payoffs for both of them which are better than maximum jsil time. So, strategically, which game are we playing: defection for one-sided gains (which likely leads to mutual defection) or cooperation for mutual gains (which likely leads for successive mutual gains)?

The former is equivalent to mutual murderous plunder in the real world; the latter is equivalent to mutual, Smithian bargaining: “Whoever offers to another a bargain of any kind proposes to do this: Give me that which I want and you shall have this which you want.” (Book 1, chapter 2, page 26, Wealth Of Nations).

Bargaining is not about promoting self-interest or selfishness or defection; it is about addressing the “self-love” of the potential bargainer by “never talk[ing] to them of our necessities, but of their advantages” (WN I.2. page 27).

Hence, placing Smith’s statements as “less illuminating than the Prisoner's Dilemma, an analysis of strategic behavior that game theorists associated with the RAND Corporation developed during the early nineteen-fifties” is both a partial misreading of the sophistication of Prisoner’s Dilemma games and a partial ignorance of Smith’s acute observations of bargaining in competitive markets.

As I have taught for years at Business Schools, as sellers or buyers we are not in competition with the seller or buyer with whom we happen to be negotiating; we are in competition with the other sellers who can supply what the buyer wants across the table, or we are in competition with the other buyers who can buy what the seller across the table is selling. Not understanding this Smithian principle of competition is so fundamental, and so widespread among some very smart economists, as to constitute an error of perspective of the first magnitude.

The “optimal joint result” requires us both to do that which is best for both of us, not what is best for us alone. John Cassidy, however, is right in his analysis of the cause of the “madness of crowds” when piling into the insanity of the recent bubble – those who stayed in cash instead, not junk derivatives, survived; those who followed the rush, lost badly. They didn’t do what was best for all of them.

Given that Smith never endorsed a policy of acting selfishly under the fantasy that whatever they did would lead to social benefits (the modern myth of the “invisible hand”), he was not likely to advise anybody to chase the modern equivalent of the “South Sea bubble”. He had a low opinion of “projectors” and “enthusiasts”. So should Smithian scholars and practitioners.

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