The linked article is a complete waste of time as the authors don’t bother to explain what the extortionate strategy is, only insist that it turns the game into an ultimatum. And the title must be a lie, since halfway through, it explicitly says TFT gets the same score as its opponent. (In other words, it doesn’t get “beat” by anything.) So the parts of the article that are true are useless, the parts that are supposedly interesting are asserted, unexplained, and the title is certainly false. Downvoted.
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.
The linked article is a complete waste of time as the authors don’t bother to explain what the extortionate strategy is, only insist that it turns the game into an ultimatum. And the title must be a lie, since halfway through, it explicitly says TFT gets the same score as its opponent. (In other words, it doesn’t get “beat” by anything.) So the parts of the article that are true are useless, the parts that are supposedly interesting are asserted, unexplained, and the title is certainly false. Downvoted.
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.