Social Psychology: Escaping the Prisoner’s Dilemma

For the past several decades the Prisoners’ Dilemma has been a dominant frame in Game Theory. It’s quadrant model has crossed the boundaries of many disciplines especially political science, economics, business, biology, computer science and philosophy. There are also the games Stag Hunt, Chicken and Hawk-Dove which are 2×2 games. My argument in this post will be that the Prisoners’ Dilemma is not adequately representative of reality.

merrillflood.jpg melvindresher.jpg

The Prisoner’s Dilemma was originally framed by Merrill Flood and Melvin Dresher while working on game theory at RAND in 1950 which Rand pursued because of possible applications to global nuclear strategy.
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Albert W. Tucker formalized the game with prison sentence payoffs and gave it the “Prisoners’ Dilemma” name (Poundstone, 1992).

The game has two prisoners who cannot communicate and each has only two moves:

  1. to conceal their guilt or
  2. reveal their guilt

They are aware of the potential outcomes of their actions as follows:

pdmatrix01.jpg

The canonical payoff matrix for the game is represented as follows:

pdmatrix025.jpg
In “win-lose” terminology represents the game in the following manner:

pdmatrix03.jpg

The flaw I see in the Prisoners’ Dilemma is that it only provides the following payoffs:

  1. Win-Win (Collaboration)
  2. Win Much-Lose Much (Exploitation)
  3. Lose Much-Win Much (Exploitation)
  4. Lose-Lose (Altercation)

It does not provide for Win-Lose or Lose-Win (Distribution). The absence of distribution may be suitable for Mutual Assured Destruction (MAD) games, but not for most other human transactions. Consequently the Prisoners’ Dilemma can be presented as follows:

pdmatrix10.jpg

Now, I am going to take a different tack with the Prisoner’s Dilemma.

ericberne1

I am going to view it from the perspective of Stephen B. Karpman’s Drama Triangle, a concept derived from Eric Berne’s Transactional Analysis. However, I am going to adhere to game theory’s premise that the players are rational.

Stephen categorized interpersonal transactions into three roles:

  1. Persecutor
  2. Rescuer
  3. Victim

In the Prisoners’ Dilemma there are only the Rescuer and the Persecutor:

pdmatrix09.jpg

In what I will call the Transaction Triangle game there are three roles and thus three moves:

pdmatrix11.jpg

In “win-lose” terminology the Transaction Triangle is as follows:

pdmatrix07.jpg

And the canonical payoff matrix is as follows:

pdmatrix12.jpg

As you can see, distribution is incorporated into the model to provide for most human transactions while still preserving the key components of the Prisoners’ Dilemma. I also concluded that the lose-lose payoff of the Ultimatum Game was suitable to provide for no transaction taking place. It is time to abandon the 2×2 mindset of mutual assured destruction and adopt a more human and realistic 3×3 game frame.

Further Reading:

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3 Responses to “Social Psychology: Escaping the Prisoner’s Dilemma”

  1. Gerhard Heise Says:

    Hello,
    first of all I like to say, that this is a great website!
    Second, I checked for literatur which deals with that dilemma. In fact I search for papers, dealing with escaping the dilemma. There must be a way out ok.
    Within the literature relevant for the papers published by globalization logicians, I gain the impression, that they just take the dilemma for the last result possible.
    SO who is the Einstein in Mathematics and Economy of today, explaining us, hwo to escape the prisoner dilemma.
    Alcazar is closed. So we need to close that prison too.
    Thanks for your attention
    Gerhard Heise
    P.O. Box 680105
    50704 Cologne
    Germany

  2. grant czerepak Says:

    Hello Gerhard,

    You are right. The prisoner’s dilemma was created to demonstrate that the only way out of annihilation through direct confrontation was cooperation.

    However, this was a deception. Indirect confrontation could occur and Afghanistan turned out to be the third player and the means to defeat the Soviets. We were suddenly dealing with a cube instead of a square and conventional conflict instead of nuclear conflict.

  3. patthechooks Says:

    Very interesting analysis. Would be fascinated to see how the Winners’ Triangle could be applied to the Prisoners’ Dilemma.
    Patrick


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