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Prisoners Dilemma Solved?

mikejuk (1801200) writes | about 2 years ago

Math 0

mikejuk (1801200) writes "Game theory is well established enough there to be no deep shocks left to surprise us, but one of the most studied games, the Prisoner's Dilemma has returned to center stage. The surprise is that there is a winning strategy — not for a single round but when the game is played repeatedly the players can attempt to maximize their “winning”. Until recently it was thought that the best strategy was the tit-for-tat ploy of simply doing what your opponent did at the last move. This gives a 50:50 split of the time in jail no matter what the opponent plays and has long been thought to justify ethical values — if you defect I’ll do the same.
Now Freeman Dyson (yes that Freeman Dyson) and William Press have discovered that tit-for-tat is just a special case of a strategy called Zero Determinant or ZD. Using a ZD strategy the player can ensure that they receive a fixed percentage of their opponents jail time no matter what they play. In tit-for-tat the percentage is 50% but the ZD player can set this at 20% or 10% so always doing better than their opponent no matter what strategy they play.
If ZD is so good why doesn’t it occur in nature? The answer is that it isn’t evolutionary stable because when two ZD players meet they do worse than ZD against any other strategy and hence when there are too many ZD players in a population it becomes a disadvantage.
One possible solution is to recognize other smart ZD players and avoid them seeking out the dumb evolutionary players instead. Could this be why intelligence evolved?
paper pdf"

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