Strip Iterated Prisoner’s Dilemma

Cogspace has posited a set of rules for strip iterated prisoner’s dilemma. Without too much ado, her rules are as follows:

Alice defects, Bob defects: Each player removes two articles of clothing.
Alice defects, Bob cooperates: Bob removes three articles of clothing.
Alice cooperates, Bob defects: Alice removes three articles of clothing.
Alice cooperates, Bob cooperates: Each player removes one article of clothing.

These rules, while a simple first-order transformation of the prisoner’s dilemma to the `strip’ format, fail to take account of the reality of the situation. That is: they assume that each player would like to remain dressed no matter what. This is not the way that the real utilities play out. The actual utilities are more like this:

  • Both strip: very high utility all around.
  • One strips: low utility for stripper, moderately high utility for spectator.
  • Neither strips: moderate utility all around.

Because of this, Katie’s analysis constitutes a transformation of the game: she has changed the pareto-optimal solution per round. This distorts the nature of the game, and thereby the set of successful strategies. Indeed, Katie’s prisoner’s dilemma is no dilemma at all!

Under the standard (non-strip) version of the game, the pareto-optimal solution (the one making everyone happiest all round) is universal cooperation. However, under Katie’s strip version, the pareto-optimal solution is universal defection. There is no reason to `cooperate’ unless you need to force your partner opponent to get naked. ‘Tit for tat grudge’ under Katie’s strip rules would work backwards: defect until the other player cooperates, and cooperate from then on.

Clearly, Katie has missed the point of `strip’ games. I’m sure that a few practical examples would be sufficient to teach her.

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About flamsmark

I do privacy at Mozilla. Years of security have left me incurably paranoid. Tech, policy, security, privacy, & anonymity are good. Open is better. GPG: 80AF07D3
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2 Responses to Strip Iterated Prisoner’s Dilemma

  1. Katie Molnar says:

    You are, of course, totally right! I just threw that post together after reading http://xkcd.com/696/. After reading your comments, I did some head-scratching but was unable to generate a set of rules that make for an interesting game. Ah well.

  2. David says:

    In order to make Strip Iterated Prisoner’s Dilemma work, all you need to do is incorporate the stripping into the defection/cooperation matrix.

    Bob and Alice are separated by a screen. Both are given the option to cooperate with the other (remove one piece of clothing) or defect (stay clothed).

    Bob and Alice both remove one piece of clothing: they stay that way.
    Bob and Alice both defect by keeping their clothes on: they are both forced to remove two items of clothing.
    Bob defects and stays clothed, Alice removes a piece of clothing: Alice is forced to remove two more items.
    Alice defects and stays clothed, Bob removes a piece of clothing: Bob is forced to remove two more items.

    This has the same set of ultimate consequences each round, but making the choice involve removing one item restores the counter-intuitive, risky nature of the original dilemma. Want to get both people naked as quickly as possible? **Don’t** strip when given the option. Want to drag out the game? Take off one piece and hope the other person doesn’t defect.

    There are other ways to do it, too, but they are variants on the original. Example: each person has the option to remove 1, 2, or 3 pieces of clothing each round; if you make the same choice as the other player then nothing changes; if you make a difference choice then whoever took off the most clothing gets to put it all back on.

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