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Abstract:
Direct reciprocity is a mechanism for the evolution of cooperation. For the iterated prisoner’s dilemma, a new class of
strategies has recently been described, the so-called zero-determinant strategies. Using such a strategy, a player can
unilaterally enforce a linear relationship between his own payoff and the co-player’s payoff. In particular the player may act
in such a way that it becomes optimal for the co-player to cooperate unconditionally. In this way, a player can manipulate
and extort his co-player, thereby ensuring that the own payoff never falls below the co-player’s payoff. However, using a
compliant strategy instead, a player can also ensure that his own payoff never exceeds the co-player’s payoff. Here, we use
adaptive dynamics to study when evolution leads to extortion and when it leads to compliance. We find a remarkable cyclic
dynamics: in sufficiently large populations, extortioners play a transient role, helping the population to move from selfish
strategies to compliance. Compliant strategies, however, can be subverted by altruists, which in turn give rise to selfish
strategies. Whether cooperative strategies are favored in the long run critically depends on the size of the population; we
show that cooperation is most abundant in large populations, in which case average payoffs approach the social optimum.
Our results are not restricted to the case of the prisoners dilemma, but can be extended to other social dilemmas, such as
the snowdrift game. Iterated social dilemmas in large populations do not lead to the evolution of strategies that aim to
dominate their co-player. Instead, generosity succeeds.
