Adaptive dynamics of extortion and compliance.
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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.
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PubMed Central - PubMed
Affiliation: Evolutionary Theory Group, Max-Planck Institute for Evolutionary Biology, Plön, Germany.
ABSTRACT
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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. Related in: MedlinePlus |
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Mentions: In order to confirm these predictions, we have simulated the dynamics in finite populations for a pairwise comparison process, where the probability to switch to the role model’s strategy is given by a Fermi function [37], [38]. We assume that mutations follow Gaussian distributions around and and focus on the distribution of strategies and on the distribution of payoffs. For we find that the population clusters around the edge of low population payoffs (see Fig. 3a), and the density function for the payoffs has a single peak at . Increasing the population size has a two-fold effect (Fig. 3b and 3c). First, compliant strategies with become stable, such that the density function of the population payoffs has a second peak at . Second, increasing the population size reduces the stochastic noise; as a consequence almost all the mass is concentrated around the two peaks and . As predicted by adaptive dynamics, and in line with previous results [23], larger populations exhibit larger payoffs. For example, payoffs for a population size exceed the payoffs for by more than a factor of six. |
View Article: PubMed Central - PubMed
Affiliation: Evolutionary Theory Group, Max-Planck Institute for Evolutionary Biology, Plön, Germany.