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.