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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.
We present tournament results and several powerful strategies for the Iterated Prisoners Dilemma created using reinforcement learning techniques (evolutionary and particle swarm algorithms). These strategies are trained to perform well against a corp
The Axelrod library is an open source Python package that allows for reproducible game theoretic research into the Iterated Prisoners Dilemma. This area of research began in the 1980s but suffers from a lack of documentation and test code. The goal o
We study the evolution of cooperation in spatial Prisoners dilemma games with and without extortion by adopting aspiration-driven strategy updating rule. We focus explicitly on how the strategy updating manner (whether synchronous or asynchronous) an
The Prisoners Dilemma game has a long history stretching across the social, biological, and physical sciences. In 2012, Press and Dyson developed a method for analyzing the mapping of the 8-dimensional strategy profile onto the 2-dimensional payoff s
We present insights and empirical results from an extensive numerical study of the evolutionary dynamics of the iterated prisoners dilemma. Fixation probabilities for Moran processes are obtained for all pairs of 164 different strategies including cl