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The Robustness of Extortion in Iterated Prisoner ’ s Dilemma ∗

Press and Dyson (2012) discovered a special set of strategies, called extortionate strategies, in the two-player Iterated Prisoner’s Dilemma. Surprisingly, a player using such strategies obtains an advantageous share of the total payoff score of the players. The other player maximizes his own score by fully cooperating, and when doing so he maximizes the score of the extortioner as well. When an extortionary player faces an evolutionary player, Press and Dyson conjecture that there always exist evolutionary paths leading to the maximum possible scores for both players. In this work we confirm their conjecture in a very strong sense. We show that not only such evolutionary paths always exist, but that actually every evolutionary path leads to the maximum possible scores, although some paths may not lead to full cooperation of the evolutionary player. This is true even in the rare cases where the setup of Press and Dyson (2012) is not directly applicable. Our result shows that extortionate strategies are even more powerful than as pointed out by their discoverers. Given our result, the extortioner is assured to receive his desired score without knowing how the other player will evolve, making it more desirable to extort.