There was a previous post about this topic that actually linked to the paper, which I think you’ll be happier with.
In particular, what the extortionate strategy does is the following: if player 2 accepts that player 1 will play the extortionate strategy, and there’s nothing to be done about that, then there is a linear relation between their scores, and he can only maximize his score by giving an even higher score to player 1. In particular, if player 2 plays TFT (which is also an extortionate strategy, in a degenerate sense, with extortion factor 1) then the two players eventually end up in the (Defect, Defect) state, and get 0 points per turn, which satisfies both relations.
All of the “ZD strategies” are described by 4-tuples of probabilities: the probabilities of cooperation given the outcome of the previous turn, which can be one of (CC, CD, DC, DD). In comments to the previous post I calculated twoexamples, and the paper contains the general formulas in equations [8] and [12].
Ah, thank you. Made that much clearer for me; I had the slightly incorrect impression that a ZD strategy was any strategy that could be described by such a 4-tuple, but I didn’t make the connection that the evolution could apply directly to the probabilities instead of the strategy that generated the probabilities.
There was a previous post about this topic that actually linked to the paper, which I think you’ll be happier with.
In particular, what the extortionate strategy does is the following: if player 2 accepts that player 1 will play the extortionate strategy, and there’s nothing to be done about that, then there is a linear relation between their scores, and he can only maximize his score by giving an even higher score to player 1. In particular, if player 2 plays TFT (which is also an extortionate strategy, in a degenerate sense, with extortion factor 1) then the two players eventually end up in the (Defect, Defect) state, and get 0 points per turn, which satisfies both relations.
How does this actually get implemented in code?
All of the “ZD strategies” are described by 4-tuples of probabilities: the probabilities of cooperation given the outcome of the previous turn, which can be one of (CC, CD, DC, DD). In comments to the previous post I calculated two examples, and the paper contains the general formulas in equations [8] and [12].
Ah, thank you. Made that much clearer for me; I had the slightly incorrect impression that a ZD strategy was any strategy that could be described by such a 4-tuple, but I didn’t make the connection that the evolution could apply directly to the probabilities instead of the strategy that generated the probabilities.