NY Times Column Misconstrues Prisoner’s DilemmaPosted: June 3, 2013
The business writer James B. Stewart’s Saturday New York Times column took a fascinating look at the situation facing a former hedge fund portfolio manager charged with insider trading who now must decide whether to cooperate with prosecutors. Stewart writes that the manager’s situation is akin to the classic game theory problem known as a prisoner’s dilemma (PD). To be sure, it’s a tricky dilemma that this fellow faces, and it resembles a PD, but unfortunately Stewart inaccurately describes the nature of a PD, and also confuses its meaning with imprecise language about “cooperation.”
The definition of a PD in the piece is incorrect. Stewart writes:
In the now-classic version, the police have arrested two suspects and are interrogating them in separate rooms. Each can either confess and implicate the other, or remain silent. If only one confesses, he goes free and the other gets a harsh sentence. If both confess, each gets a reduced sentence, but still goes to jail. If neither confesses, the government lacks the evidence needed to convict and both go free.
This misrepresents the canonical PD structure, which has a payoff for cooperating with the other suspect (staying silent) that needs to be less than (not equal to) the payoff for defecting (confessing) if other suspect cooperates (stays silent). To put it another way, the payoff for solo defection has to exceed the payoff for mutual cooperation. But in the Times piece Stewart describes the “classic version” as a situation where suspect goes free if both stay silent, and goes free if only he confesses. Those are equivalent outcomes – “goes free.”
In PD structure terms (this graphic from the Wikipedia entry on PD),
T has to be greater than R. This is not a trivial problem. By having T=R (as Stewart suggests), any temptation to defect is removed – it never makes sense to defect. You could say it takes the D out of PD!
In addition to erroneously describing a classic PD, the piece is confusing because in the context involved – turning state’s evidence – Stewart understandably and repeatedly uses the word “cooperate” (as in: the guy will or won’t cooperate with prosecutors). But this leads to a problematic passage like this one:
Game theorists have demonstrated that the rational choice, or dominant strategy, is always to confess and implicate the other, even though the optimal outcome for both occurs if neither cooperates. That’s because, as Professor Picker explained, if one prisoner has confessed, the best the other can hope for is also to confess and get the moderate sentence rather than the harsher sentence reserved for those who don’t cooperate. If one prisoner doesn’t confess, the other can go free by implicating him. Although they collectively are better off if neither cooperates, their individual self-interest dictates cooperation.
The problem is that in the game theory/PD world, “cooperates” means stays silent (you cooperate with your fellow suspect; confession is defection). So when Stewart writes in the first sentence of this passage that “the optimal outcome for both occurs if neither cooperates,” he means cooperates with the prosecutor, not cooperates in the PD sense (stay silent). The last sentence in the passage sums it up correctly in terms of “cooperating” with the prosecutor, but wrongly in PD language – exactly the opposite is true in the cooperate/defect sense of PD.