Teaching the ABA Journal some game theory

The ABA Journal:

In a rare real-life, high-stakes demonstration of the prisoner’s dilemma—two suspects can both escape consequences, but only by trusting each other not to snitch to authorities—a judge in Malaysia has freed a man facing the gallows in a drug-trafficking case.

That’s because, due to a police error, no one but the suspect—and his brother, who is his identical twin—knows which man should be tried in the case, according to the Telegraph. DNA testing would not have helped, because identical twins have the same DNA.

Of course, this is not an actual demonstration of the prisoner’s dilemma. The two-person one-shot prisoner’s dilemma is characterized by the following payoff matrix (where player 1 chooses between rows and player 2 chooses between columns, and player 1’s payoff is listed first):

Cooperate Defect
Cooperate Q,Q S,P
Defect P,S R,R

such that P>Q>R>S

In such a case, the only Nash equilibrium is mutual defection, and the prisoners snitch on one another.

In the instant case, however, P=Q. If one brother stays silent and the other brother snitches, the brother who snitches does no better than he would have if he stayed silent.* That means there are two nash equilibria: mutual cooperation and mutual defection. And that is why the two brothers could (although need not) have rationally not snitched on one another, and thus why they’re not in jail. Because it wasn’t a prisoner’s dilemma! Grrr. Bad ABA Journal.

It is also wrong to say that real-life, high-stakes prisoners dilemmas are rare. But that’s a whole ‘nother ball of wax.

* It’s also not at all clear what the value of R is, relative to the others. If both brothers snitch, do they still get off? Or do they just each have some positive probability of getting convicted, depending on who the jury believes, s.t. P=Q>R>S? In either case, however, there are two Nash equilibria, mutual cooperation and mutual defection.


2 Responses to “Teaching the ABA Journal some game theory”

  1. x. trapnel Says:

    You ever read the ‘Newcomb’s Problem as P-D’ mini-debate? I think Nozick started it. I think one issue was: does the problem change if it’s two identical twins?

  2. Paul Gowder Says:

    I’ve seen little bits of that fly past my windshield and skimmed them. Wasn’t Lewis in on that one for a while too? And/or Stalnaker? That’s one of those things about which I’ve thought “I should really get a closer look at when I find the time” for a long while.

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