3.06.2011

The Prisoner’s Dilemma and Crime- Russ Stover


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02-14-2011
            Anyone who has ever seen CSI, NCIS, Law & Order, or one of their imitators has watched as two criminal suspects are arrested then separated and questioned.  Each is told the other is turning state’s evidence and making a deal and that if they don’t do the same they are look at a long prison sentence, or worse.  This is the Prisoner’s Dilemma, a fundamental problem and example of game theory.
  Game theory tries to explain why two (or more) people choose not to cooperate even when it is in their best interests.  The game was developed by Merrill Flood and Melvin Dresher of the Rand Corporation in 1950 and built upon game theory developed by John von Neuman and Oscar Morgenstern, also of Rand.  Albert Tucker added a narrative to the problem to help in understanding:
Two people are arrested.  The police do not have enough evidence and separate the prisoners for questioning.  Each of them is offered the same deal.  Testify against the other (defection in game theory parlance) while the other does not (cooperates) and the defector went free while his accomplice got ten years in prison.  If neither talk they only get six months.  If both defect and betray each other they each get a five year sentence.  They each have to choose whether to talk or not to their possible benefit or possible detriment. 
If each only cares about themselves, as criminals are wont to do, then we have a zero-sum game, which is where two players either cooperate with the other or defect against them.  Each wants only to maximize their own payoff and doesn’t care about the other.  In this version of the game defecting dominates cooperating, with both defecting putting the game in equilibrium—each gets the best they can in light of the other’s decision.  In any situation defecting alone is better than cooperating then it is only rational to defect and if the other prisoner comes to the same rational conclusion both defect, putting the game in equilibrium.
It can be summarized in a table:

Prisoner B Remains Silent
Prisoner B Talks
Prisoner A Remains Silent
Each gets 6 months
A gets 10 years, B goes free
Prisoner A Talks
A goes free, B gets 10 years
Each gets 5 years
Here A and B get lighter sentences if they both talk (lower right corner).  A can rationalize that whatever B’s decision he is better off talking than remaining silent.  If B makes the same rationale they both betray each other and get a lower sentence than if one had talked and one had not. 
In criminology investigators may be able to apply the dilemma almost verbatim to two prisoners.  Marek Kaminski, a game theorist and former political prisoner, analysed the game as set up  by a prosecutor.  He found that while the Prisoner’s Dilemma is the perfect game for a prosecutor, there are many psychological and emotional factors that can strongly affect the payoffs and changes the dynamics of the game.  The defect/defect outcome of the Prisoner’s Dilemma is why plea bargaining not used in many countries.  It is in the interest of both suspects to confess against the other, but if one is truly innocent they will also go to prison.

References
Poundstone, W. (1992) Prisoner’s dilemma.  Doubleday, NY, NY.

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1 comment:

  1. Here you mention 'questioning'. Let's be frank about the techniques used by police and especially by FBI et al. They move from questioning into interrogation very quickly.

    ReplyDelete

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