The robustness of zero-determinant strategies in Iterated Prisoner׳s Dilemma games

In this work we confirm their conjecture in a very strong sense, not just for extortionate strategies, but for all ZD strategies that impose positive correlations between the players׳ payoffs. We show that not only the conjectured adapting paths always exist, but that actually every adapting path leads to the maximum possible scores, although some paths may not lead to the unconditional cooperation by the adapting player. This is true even in the rare cases where the setup of Press and Dyson is not directly applicable. Our result shows that ZD strategies are even more powerful than as pointed out by their discoverers. Given our result, the player using ZD strategies is assured that she will receive the maximum payoff attainable under the desired payoff relation she imposes, without knowing how the other player will evolve. This makes the use of ZD strategies even more desirable for sentient players.