#### Super? Super Rational.

The question of morality came up, but I think it is irrelevant here. Game theory and the PD are about strategy or set of moves, maximization in terms of the constraints of the problem...and in this problem it is to maximize your benefit (money).

We'll get back to this problem in a moment. Game theory and strategy can take several forms given the assumptions that are made. If communication is allowed, the skill level of the other 'gamers', if the game is co-operative or not, if there is perfect information, if the game is simultaneous or sequential, etc. Fundamentally, it is making decisions about what you think the other gamer(s) will do.

IMHO, this single-shot problem has a nash-esque equilibrium. In other words, your choice constitutes the best response to the actions of other players or you do what is best for yourself and the group. This is the rational equilibrium. I ran 10,000 simulations using simple binomial (p) distribution to model the anticipated choice of the other gamers and here are the results I got using Hofstader's 20 player PD and the payoff matrix below.

paverage C payoutaverage D payoutaverage payout
0.1051.374.352.1
0.2542.775.648.3
0.5028.557.040.4
0.7514.238.130.3
0.905.825.723.2

p is the anticipated probability that the other gamers choose Defect. As Hofstader expected, everyone would choose to Cooperate in order to maximize the group payout. But this is if you assume that every player is rational and informed.

A better assumption, is that you can't predict what other gamers will do. In other words, you predict that other gamers will be equally likely to Cooperate or Defect, in which case you Defect. This may explain why Hofstader experiment resulted in so many Defectors in his sample of "super" rational thinkers.

Maybe, they would all cooperate if they were super super rational. (This seems like the beginning of some bad time travel movie).

permalink | posted by sourat | 11.28.2006 |