Evolutionary Extortion and Mischief: Zero Determinant strategies in iterated 2x2 games

Abstract: This paper studies the mechanisms, implications, and potential applications of the recently discovered class of Zero Determinant (ZD) strategies in iterated 2x2 games. These strategies were reported to successfully extort pure economic maximizers, and to mischievously determine the set of feasible long-term payoffs in iterated Prisoners' Dilemma by enforcing linear constraints on both players' expected average scores. These results are generalized for all symmetric 2x2 games and a general Battle of the Sexes, exemplified by four common games. Additionally, a comparison to conventional strategies is made and typical ZD gameplay simulations are analyzed along with convergence speeds. Several response strategies are discussed, including a glance on how time preferences change previous results. Furthermore, a possibility of retaliation is presented: when maximin scores exceed the minimum symmetric payoff, it is possible to extort the extortioner. Finally, a summary of findings from evolutionary game theory shows that mischief is limited by its own malice. Nevertheless, this does not challenge the result that mindless economic maximization is subject to extortion: the study of ZD strategies reveals exciting new perspectives and opportunities in game theory, both evolutionary and classic.