The Prisoner’s Dilemma

The prisoner’s dilemma as a briefcase exchange

(I think the PD sheds light on so much of human life. We continuously find ourselves in situations with its structure. Here is a brief explanation of the PD.)

 Game Theory

For our purposes, a game is an interactive situation in which individuals, called players, choose strategies to deal with each other in attempting to maximize their individual utility. There are several ways of distinguishing games including: 1) in respect to the number of players involved; 2) in respect to the number of repetitions of play; 3) in respect of the order of the various player’s preferences over the same outcomes. On the one extreme are games of pure conflict, so-called zero-sum games, in which players have completely opposing interests over possible outcomes. On the other extreme are games of pure harmony, so-called games of coordination. In the middle are games involving both conflict and harmony in respect of others. It is one particular game that interests us most, since it describes the situation in Hobbes’ state of nature, and is the central problem in contractarian moral theory.

The Prisoner’s Dilemma

The prisoner’s dilemma is one of the most widely debated situations in game theory. The story has implications for a variety of human interactive situations. A prisoner’s dilemma is an interactive situation in which it is better for all to cooperate rather than for no one to do so, yet it is best for each not to cooperate, regardless of what the others do.

In the classic story, two prisoners have committed a serious crime but all of the evidence necessary to convict them is not admissible in court. Both prisoners are held separately and are unable to communicate. The prisoners are called separately by the authorities and each offered the same pro-position. Confess and if your partner does not, you will be convicted of a lesser crime and serve one year in jail while the unrepentant prisoner will be convicted of a more serious crime and serve ten years. If you do not confess and your partner does, then it is you who will be convicted of the more serious crime and your partner of the lesser crime. Should neither of you confess the penalty will be two years for each of you, but should both of you confess the penalty will be five years. In the following matrix, you are the row chooser and your partner the column chooser. The first number in each parenthesis represents the “payoff” for you in years in prison, the second number your partner’s years. Let us assume each player prefers the least number of years in prison possible. In matrix form, the situation looks like this:

Prisoner 2

        Confess  Don’t Confess
 Prisoner 1 Confess (5, 5) (1, 10)
  Don’t Confess (10, 1) (2, 2)

So you reason as follows: If your partner confesses, you had better confess because if you don’t you will get 10 years rather than 5. If your partner doesn’t confess, again you should confess because you will only get 1 year rather than 2 for not confessing. So no matter what your partner does, you ought to confess. The reasoning is the same for your partner. The problem is that when both confess the outcome is worse for both than if neither confessed. You both could have done better, and neither of you worse, if you had not confessed! You might have made an agreement not to confess but this would not solve the problem. The reason is this: although agreeing not to confess is rational, compliance is surely not rational!

The prisoner’s dilemma describes the situation that humans found themselves in in Hobbes’ state of nature.1 If the prisoners cooperate, they both do better; if they do not cooperate, they both do worse. But both have a good reason not to cooperate; they are not sure the other will! We can only escape this dilemma, Hobbes maintained, by installing a coercive power that makes us comply with our agreements (contracts). Others, like the contemporary philosopher David Gauthier, argue for the rationality of voluntary non-coerced cooperation and compliance with agreements given the costs to each of us of enforcement agencies. Gauthier advocates that we accept “morals by agreement.”

1Some scholars argue that Hobbes’ state of nature is best described as an assurance game.

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3 thoughts on “The Prisoner’s Dilemma

  1. A very interesting subject Dr. Messerly, thank you for presenting it!

    ” If the prisoners cooperate, they both do better; if they do not cooperate, they both do worse. ”
    Surely this applies to all of mankind’s interactions? It is true we don’t know what the other fellow will do, we can only control our own behavior and our collective behavior is dictated by our ‘personal’ morals, so, no two people will react exactly the same in every situation.
    Wise people try and limit their exposure to irrational behavior by controlling the situations, and people, they interact with!

    David Gauthier argues for the rationality of voluntary non-coerced co-operation and compliance, well that does ‘sound’ good, I’m sure a robber would prefer that you voluntarily hand him your wallet when he approaches you with his eyebrow raised and his hand outstretched, and not make a situation that is already stressful and difficult for each of you more difficult by making him attempt to coerce you compliance, remember ‘Nice’ people want to get along and not create a scene!
    Gauthier advocates that we accept “morals by agreement” it would be great if we could only ‘actually’ do that, then we could actually de-fund the police, and save the costs, to us all, of paying for the “enforcement agencies” !

  2. After all, the Internet we are using right now was built by DARPA and Business—not the love of Christ or the equanimity of Gautama.

  3. Maybe some wise person would care to comment on the following line of thought: Donald Trump (DT) is an expert at using game theory to maximize benefits for himself in life.

    My reasoning is that DT, being a very high IQ sociopath/narcissist, is able and willing to go much further in the direction of anti-social and anti-cooperative behavior than most politicians and businessmen.

    And this extreme approach to life has worked pretty well for him.

    His skillfully executed extreme antisocial ways have made him extremely wealth, made him a top-tier celebrity, and got him elected president once (so far).

    DT is also capable of acting in social ways that have led him to be able to build a national, 50-state movement centered on himself and his ego. His core followers in his movement are reportedly people like him, i.e., people who tend to be toward the “pathological” end of the scales of sociopathy and narcissism.

    Many of us are appalled by the harm that DT does to our many of our fellow citizens, and to our culture, and to our future.

    But DT is not appalled by what he has done and is doing. He is playing a game, purely and simply, and playing it to win (for his own benefit and no one else’s benefit), and, across the span of his life, he has mostly been winning.

    I tried to persuade my brother that a certain percentage of our fellow Americans just don’t care if the USA or human civilization ceases to exist in 50 or 100 years, and just don’t care if innocent people in the present time suffer unnecessarily because of the actions or inactions of government or businesses. But my brother couldn’t accept this as a calming or clarifying explanation of what’s going on. All he could do was feel and express hate for right-wing people.

    When I began studying philosophy, I assumed it would provide compelling arguments for why all human beings should be highly pro-social and pro-justice (as per the values of typical modern American liberal). But now I don’t think that philosophy provides compelling reasons for that at all. People who want to approach life in a harsh, brutal, “Darwinian” way are under no compulsion from logic, reason, science, or philosophy to change their ways. (Religion, by contrast, does propose authoritative condemnations of brutality, but most or many modern people think gods and God are nothing but fairy tales.)

    Yet, typical Liberals, Progressives, Socialists, etc., spend much time being outraged about people like DT, and seem certain that people like DT are somehow ignorant, uneducated, and uninformed, or perhaps psychologically damaged, and that they could be corrected with education, philosophical counseling, or psychotherapy.

    But, in fact, DT is quite happy. I think DT is probably even happier on a daily basis than I am. I read a study saying that highly narcissistic people, when they take a daily life satisfaction quiz, score higher than most other people.

    DT is quite logical. Over the decades, in many books and interviews, he has expressed his worldview in terms that I would describe as very sophisticated and philosophical.

    We may look at people like DT, who are highly functional, highly successful, highly productive, and highly destructive and dangerous, and label them “sociopath” and “immoral” and “monsters,” but they just laugh and don’t care.

    They reason: “I’m winning.”

    They reason: “These critics of mine are just losers and nobodies who feel that they must attack people who have personal power and fame, since they want such power and fame but can never attain such.”

    They reason: “These critics of mine are like little mice who just want to be safe all the time; they don’t realize that joy in life comes from living dangerously.”

    Game theory does seem to assume that everyone operates in life just exactly as DT operates: purely to maximize one’s own benefits, without any real concern for the well-being of other players in the game.

    So, if we believe in game theory, why do we so harshly judge and condemn DT?

    Shouldn’t we set aside our strong emotions, and just organize ourselves and our allies to play the game to defeat DT and other people in the game who are working for social, political, economic, and ecological outcomes that we don’t like?

    And doesn’t all this mean that moral philosophy and political philosophy, as these have been traditionally understood since Plato, are of little or no use in defeating people like DT?

    If life is a game (as game theory assumes), and nothing more, isn’t philosophy just a waste of time?

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