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:
B
(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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