Saturday, May 26, 2012

mildly mathematical: the prisοner's dilemma, iterated.

i'm not usually one for discrete mathematics, but this title/abstract caught my attention.
Iterated Prisοner’s Dilemma contains strategies that dominate any evolutionary opponent (William H. Press and Freeman J. Dysοn)


The two-player Iterated Prisοner’s Dilemma game is a model for both sentient and evolutionary behaviors, especially including the emergence of cooperation. It is generally assumed that there exists no simple ultimatum strategy whereby one player can enforce a unilateral claim to an unfair share of rewards.

Here, we show that such strategies unexpectedly do exist. In particular, a player X who is witting of these strategies can (i) deterministically set her opponent Y’s score, independently of his strategy or response, or (ii) enforce an extortionate linear relation between her and his scores.
Against such a player, an evolutionary player’s best response is to accede to the extortion. Only a player with a theory of mind about his opponent can do better, in which case Iterated Prisοner’s Dilemma is an Ultimatum Game.
what is odd for me is allowing a "theory of mind."  being a mathematician, if a mechanism isn't well-defined, then it is forbidden from use.  as long as we're allowing these vague matters into the discussion, however, it makes me wonder:
is Player X's extortion also an instance of mind?
say that both X and Y have the same extortion mechanism; will it be anymore effective?
of course, maybe i should just read the article.  i mean, it's only 5 pages long.  the cool thing is that the article is available @PNAS via open access [1] .. so anyone(!) can read it. (-:

(also, does anyone think it .. er, telling .. that in the abstract, Player X is male and Player Y is female?)

[1] on a related note, there is a petition to make all taxpayer-funded research available online for free.  if you think it will make a difference, then the link is here (but it requires an account and username).

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