Wednesday, March 26, 2008

The Prisoner's Dilemma

The Prisoner's Dilemma is what makes ethics interesting. It's an apparent paradox. Given some game with the payoff matrix:
CooperateDefect
Cooperate3,30,5
Defect5,01,1

A rational person would prefer the Cooperate/Cooperate outcome [Pareto optimum] (and gain 3) to the Defect/Defect outcome (and gain 1). However, it is the dominant strategy to defect [Nash Equilibrium]: for either of my opponent's strategies, defection always has the higher payoff to me. If my opponent defects, then I win 1 if I defect instead of 0 if I cooperate; if my opponent cooperates then I win 5 if I defect instead of 3 if I cooperate. Of course, defection is my opponent's dominant strategy as well. So on one analysis, Cooperate/Cooperate is the preferred outcome; on another analysis, Defect/Defect is the preferred outcome.

There are two ways to resolve the Prisoner's Dilemma for the Pareto optimum. The first is to iterate the game an indefinite number of times and play "tit-for-tat". But it's not always possible to iterate a game indefinitely.

The second is to change the game by changing the payoff matrix, usually by threatening external punishment for defection. For example, if the townspeople agree to get together and beat either of us senseless if either cheats in a closed bag exchange, then we've changed the payoff for defection from 0,5 to 0,-1000, making cooperation the dominant strategy, and making one choice unambiguously rational (the Pareto optimum is also the Nash Equilibrium).

However, if you can change the game in one way, you can change it in other ways. We can just as easily change the game so that it's asymmetric, making it for instance always rational for brown-eyed people to cooperate and blue-eyed people to defect by punishing only brown-eyed people for defecting. Changing the low-level game just makes another Prisoner's Dilemma at a more abstract level: Cooperate becomes "make the game symmetric" (or make good laws/obey the law); "Defect" becomes "make the game asymmetric" (or make bad laws/disobey the law); the Nash Equilibrium is for the authority to make bad laws and the subjects to disobey them.

For this reason, purely authoritarian approaches to solving the Prisoner's Dilemma always fail. The authority will try to change the game for its exclusive benefit, sooner or later depending on how rational and intelligent the authority is; the subjects will then resist the authority. Authoritarian solutions to the Prisoner's Dilemma are dynamically unstable.

To a certain extent, religion can coerce the Cooperate/Cooperate outcome by changing the game: God will punish you for defecting and/or reward you for cooperating (and perhaps reward you more if your opponent defects). This is the sense I spoke of earlier of how religion could have an overall beneficial effect. The effect is weak; religion is a dynamically unstable authoritarian strategy.

(Pseudo-authoritarian solutions are possible, but only where you have competing authorities, who themselves play tit-for-tat. However, within-authority conflicts will always revert to the Nash Equilibrium.)

Democracy is a clever way of solving the Prisoner's Dilemma in a dynamically stable way. The people and the government play a abstract-level game of tit-for-tat — we need to make sure that only one abstract-level authority/submission game is iterated — and can thus implement any number of concrete-level Pareto optima where direct iteration is impractical. Of course, like any system in dynamic equilibrium, democracy is susceptible to sufficiently large "random" forces to push it to a state where the equilibrium cannot be maintained. If the government becomes too powerful, the people cannot "punish" the government sufficiently and the government can "defect" with impunity; likewise a too-weak government invites the people to "defect" into anarchy and chaos.

7 comments:

  1. I think with a small enough community, there is concern about tit for tat in that if you're an asshole who always defects, you'll get a bad rep in the community that you may not want - but if you are in a huge city where you can be annonymous, then have at it - you can always find more suckers.

    I also wonder, if there are simply people who, by nature, like to cooperate, and a bunch of them play, they'll end up racking up the points (resources) much more than those who use the defect strategy - because eventually tit for tatters will wipe out the defecters (or at least keep them down to 1s) as the suckers are all used up or switch. You simply can't consistently get 5 over and over again as a defector - eventually your luck runs out and people are not going to be happy with you. But you could cooperate and get 3's forever with another cooperator...

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  2. I am afraid that I do not find the prisoner's dilemma to make ethics interesting. In fact, I seldom find its relevance to ethics. It is a highly contrived situation that some skillful interrogators may put into practice to extract confessions from the accused, but it does not describe a real-world situation.

    We see this particularly in the iterated form - where individuals have repeated encounters. There is a whole list of problematic assumptions.

    (1a) It assumes that people know what the payoffs are in advance - that these beliefs are accurate.

    (1b) It does not take into consideration the possibility of lying about facts relevant to the payoffs.

    (2) It assumes that each exchange has the same payoffs. That is to say, it does not investigate the strategy of cooperating when there are small payoffs and defecting when there are big payoffs.

    (3) It assumes that the other party always knows of a defection.

    In addition, your second option of 'changing the game' looks at one possible way of changing the matrix. It does not look at a second option.

    That option is simply to change what agents desire. For example, give each agent a desire for cooperation and an aversion to defection. This increases the score for cooperation options and decreases the score for defection options, so that prisoner dilemma type situations simply do not occur.

    This second option is where I find morality. Morality is not concerned with finding ways to resolve prisoners' dilemmas. It is concerned with finding ways to avoid them.

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  3. DBB: if you are in a huge city where you can be annonymous, then have at it - you can always find more suckers.

    Precisely. The iterated PD assumes the same agents (or a closed, mutually interacting group of agents) are iterating the game. If I can always move on to a new opponent, the game becomes non-iterated. (Or iterated a definite, known number of times, which is the same thing.)

    if there are simply people who, by nature, like to cooperate, and a bunch of them play, they'll end up racking up the points (resources) much more than those who use the defect strategy.

    Yes indeed. Read the Wikipedia article; that's an experiment that's been performed.

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  4. Alonzo: I am afraid that I do not find the prisoner's dilemma to make ethics interesting.

    I'm not surprised. You and I rarely (if ever) see eye-to-eye about ethical philosophy.

    [The PD] does not describe a real-world situation.

    Here are some examples.

    There is a whole list of problematic assumptions.

    All of the assumptions you list talk about different kinds of games. Perhaps I over-spoke a little in the lede; I didn't mean to say that the PD is the only thing that makes ethics interesting.

    That option is simply to change what agents desire. For example, give each agent a desire for cooperation and an aversion to defection.

    To give agents desires requires neurosurgery and brainwashing considerably more technological prowess than we have now. It is not a "simple" matter at all.

    And, unlike you, I'm not particularly thrilled about anyone giving (or taking away) my own or anyone else's desires. The concept seems quite totalitarian to me.

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  5. Morality is not concerned with finding ways to resolve prisoners' dilemmas. It is concerned with finding ways to avoid them.

    No, you personally are not concerned with finding ways to resolve Prisoner's Dilemmas. Happily, philosophical inquiry continues without your permission.

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  6. Happily, philosophical inquiry continues without your permission.

    But not without Mine! Stop it!

    Sincerely,

    God

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  7. That's hilarious! Thanks for the laugh. Brilliant.

    ReplyDelete

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