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The Evolution of Extortion in Iterated Prisoner's Dilemma Games
Iterated games are a fundamental component of economic and evolutionary game
theory. They describe situations where two players interact repeatedly and have
the possibility to use conditional strategies that depend on the outcome of
previous interactions. In the context of evolution of cooperation, repeated
games represent the mechanism of reciprocation. Recently a new class of
strategies has been proposed, so called 'zero determinant strategies'. These
strategies enforce a fixed linear relationship between one's own payoff and
that of the other player. A subset of those strategies are 'extortioners' which
ensure that any increase in the own payoff exceeds that of the other player by
a fixed percentage. Here we analyze the evolutionary performance of this new
class of strategies. We show that in reasonably large populations they can act
as catalysts for the evolution of cooperation, similar to tit-for-tat, but they
are not the stable outcome of natural selection. In very small populations,
however, relative payoff differences between two players in a contest matter,
and extortioners hold their ground. Extortion strategies do particularly well
in co-evolutionary arms races between two distinct populations: significantly,
they benefit the population which evolves at the slower rate - an instance of
the so-called Red King effect. This may affect the evolution of interactions
between host species and their endosymbionts.Comment: contains 4 figure
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