  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.
