Friday, April 19, 2013

Dilemma 15: Freeing the Prisoner

Part 3: 
Dilemma Theory

Freeing the Prisoner

The non-zero-sum game Dilemma usually goes by the name “prisoner’s dilemma”. In this book I drop the first part of that name; partly for brevity, but also to transcend the pessimism implicit in the name “prisoner’s” dilemma. I believe that we need not fear this dilemma. By accepting dilemma as it is, we become free.
Dilemma was first popularized as a non-zero sum game involving two prisoners, interrogated separately by the authorities. Each prisoner was offered a reduced sentence if he informed; but if both inform on each other, then both do worse than if they had both remained silent.
The “payoff” (really, penalty) matrix is:


(A,B)            | silence   squeal
silence    |   1,1  |   3,0   |      
A               -|--------|---------|      
 squeal    |   0,3  |   2,2   | 

The numbers refer to years spent in prison, which both players want to minimize. (Oddly enough, this matrix still defines a dilemma when both players strive to maximize the numbers! The negative of a dilemma is a reversed-poles dilemma.)

If both players reason egotistically, each will deduce that squealing is better, no matter what the other does; but such egotistical reasoning leads to draw, the “Nash equilibrium”. It is an equilibrium because neither side can improve on it unilaterally. Like it or not, two egotists will find themselves stuck there; yet truce is better for both!
It is this conundrum, not the Gothic theatrics surrounding “prisoner’s” dilemma, which gives dilemma theory its unique urgency. How do rational players rise to the state of truce? The possibility of mutual profit raises the question of mutual aid. How do we nurture cooperation?
It’s as if the prisoners, mired in draw, were taunted by the spectre of truce, hovering just overhead, as part of their punishment. If only the prisoners worked together, then their dilemma would no longer be a prison. They’d be free! How then do we free the prisoners? I see three ways:
1) Play it out: Truce the Tournament
2) Walk away: the Option of Leaving
3) Break the game: Whistle-Blowing
I discuss option 1 in the “The Shadow Of The Future”. Repeated play makes negotiation possible via reciprocation.
I discuss option 2 in “The Unexpected Departure”. In general, option 2 improves play in Dilemma; if players may leave a dilemma tournament at any time, then that weeds out those unwilling to take a long view of their actions.
Option 3 refers to an instance of heroic resistance to dilemma exploitation. It is the story of the Doctor from Kharkov, and it is told in the following story; “Implicate the Interrogator.”

Implicate the Interrogater

During Stalin’s Great Purge, prisoners were offered the chance to reduce (though never cancel) their sentences by implicating others. Stalin exploited social disunity to impose a reign of terror; thus the purge spread.
The Doctor from Kharkov, when brought to his interrogator, proceeded to name every doctor in the town of Kharkov (for he had a good memory). The interrogator, appalled at the prospect of losing every doctor in town, asked the Doctor to reduce the list to a more manageable size; the Doctor refused, and was thrown into prison.
From prison he wrote a letter denouncing his interrogator; after all, he had asked the Doctor, a confessed traitor, to leave names off his indictment list! This way the Doctor left Stalin with no consistent course of action. Shall Stalin punish the prisoner or the interrogator, or both, or neither? If only one, which one? If neither, then does that not leave a loophole in the purge, through which real traitors could slip? And if both, then doesn’t that raise the cost of the purge?
The good Doctor’s tactic of implicating the interrogator was soon copied elsewhere; and the Purge soon came to a halt. Some have argued that the Purge had accomplished Stalin’s purpose by then anyhow; but none deny that the implication tactic was instrumental in ending the Purge at that time.

So you don’t have to be imprisoned by a dilemma; if you don’t like the game, you can walk away from it or bust it up.

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