Recognising and evaluating the effectiveness of extortion in the Iterated Prisoner's Dilemma

Since the introduction of zero-determinant strategies, extortionate strategies have received considerable interest. While an interesting class of strategies, the definitions of extortionate strategies are algebraically rigid, apply only to memory-one strategies, and require complete knowledge of a strategy (memory-one cooperation probabilities). We describe a method to detect extortionate behaviour from the history of play of a strategy. When applied to a corpus of 204 strategies this method detects extortionate behaviour in well-known extortionate strategies as well others that do not fit the algebraic definition. The highest performing strategies in this corpus are able to exhibit selectively extortionate behavior, cooperating with strong strategies while exploiting weaker strategies, which no memory-one strategy can do. These strategies emerged from an evolutionary selection process and their existence contradicts widely-repeated folklore in the evolutionary game theory literature: complex strategies can be extraordinarily effective, zero-determinant strategies can be outperformed by non-zero determinant strategies, and longer memory strategies are able to outperform short memory strategies. Moreover, while resistance to extortion is critical for the evolution of cooperation, the extortion of weak opponents need not prevent cooperation between stronger opponents, and this adaptability may be crucial to maintaining cooperation in the long run.