Thursday, September 16, 2010

Prisoner's Dilemma -- and permutations

In game theory's original, single-play, Prisoner's Dilemma problem, two prisoners each are given the choice between silence and betrayal of the other. The optimal choice is betrayal -- and therein lies a paradox.  Volume 1.3 of the online journal Unsplendid includes the following poem by Isaac Cates that reveals the nature of this classic decision dilemma.

   The Prisoners' Dilemma

   It's like the Prisoners' Dilemma: caught
   together, questioned separately, two accomplices
   have one faint chance to set the cops on their ears.
   There is no evidence. Without a confession,
   there's nothing concrete on either. The cops thus offer

   A———, if she gives up B———, takes advantage of her
   too-trusting partner, a low-security cot
   for, say, two measly years; on her confession
   B——— gets twenty. Meanwhile, her accomplice
   gets the same deal poured like strychnine in his ears:

   inform on her, gain maybe eighteen years.
   Should both the suspects take the D.A.'s offer,
   both get ten; yet if neither accomplice
   turns rat, if both trust in trust, they both go scot-
   free. Yes, that would be best. Must A———'s confession

   admit it can't trust B——— not to confess in
   his tense isolation, although his willing ears
   received her whispers on the night they were caught
   like conch-lips catching on the ocean's offer?
   Honor among thieves? Believe, my dear accomplice,

   what just a little trust here could accomplish:
   our confidence-games turning to confession,
   admission. We each suspect the other suffers
   certain suspicions. At night, at times, our ears
   have been burning. Must we be wrought up, caught

   like truants' ears, pinched by the cops, or caught
   referring to each other as accomplices
   before we hear our own confessions?

Notice that the end-words of each stanza are permutations of the same (approximately) five words throughout the first five stanzas and then each of these words appears once in the final three line stanza.  (Numbering the end words of a given stanza using 1-2-3-4-5 then the end words of the next stanza are 5-1-4-2-3,)  This poem's format resembles a sestina except that instead of six six-line stanzas we have five five-line stanzas.)

For additional paradoxes (and poems about some of them) see the September 7 posting, Against Intuition
One more thing:  Prisoner's Dilemma also is the title of a  novel  (1988) by Richard Powers that I much enjoyed.

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