Note that, actually, playing ALL D in an environment in which everybody else uses TFT would not result in winning the tournament. For simplicity, let’s ignore the fact that everybody gets paired once with RANDOM. Let’s use Axelrod’s parameters of 200 iterations and payoffs of 5, 3, 1, and 0, and assuming there are n players in the tournament, one who uses ALL D and the remaining n-1 using RANDOM, each TFT player would achieve a total payoff of 3 x 200 x (n-1) + 199 = 600n – 401, while the ALL D player’s total would be (5 + 199) x (n-1) + 200 = 204n – 4, which is lower for all value of n>1. What’s happening here is that two TFTs roll up huge payoffs (600) together, while ALL D “beats” TFT but achieves only a low payoff (204) in doing so.
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