Satisfied-Defect, Unsatisfied-Cooperate: A Novel Evolutionary Dynamics
  of Cooperation Led by Aspiration

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Abstract

The evolutionary game theory has been widely used to study the evolution of cooperation in social dilemmas where imitation-led strategy updates are typically assumed. However, results of recent behavioural experiments are not compatible with the predictions based on the imitation dynamics, casting doubts on the assumption of the imitation-led updates and calling for alternative mechanisms of strategy updates. Although an aspiration-led update is often considered as an alternative to the imitation-led one, they are still similar in that both yield cooperation less abundant than defection in Prisoner's Dilemma games. While details of update rules can have significant impacts on the evolutionary outcomes and many variations in imitation-led updates are thus studied, there exist few alternatives in aspiration-led updates. We introduce a novel aspiration-led update mechanism (`Satisfied-Defect, Unsatisfied-Cooperate') that is psychologically intuitive and yields cooperation to be more abundant than defection in Prisoner's Dilemma games. Using analytical and numerical methods, we study and link the stochastic dynamics of it in finite populations and the deterministic dynamics of infinite populations.

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A simple rule for the evolution of cooperation on graphs and social networks.

Hisashi Ohtsuki, Christoph Hauert, Erez Lieberman … (2006)

A fundamental aspect of all biological systems is cooperation. Cooperative interactions are required for many levels of biological organization ranging from single cells to groups of animals. Human society is based to a large extent on mechanisms that promote cooperation. It is well known that in unstructured populations, natural selection favours defectors over cooperators. There is much current interest, however, in studying evolutionary games in structured populations and on graphs. These efforts recognize the fact that who-meets-whom is not random, but determined by spatial relationships or social networks. Here we describe a surprisingly simple rule that is a good approximation for all graphs that we have analysed, including cycles, spatial lattices, random regular graphs, random graphs and scale-free networks: natural selection favours cooperation, if the benefit of the altruistic act, b, divided by the cost, c, exceeds the average number of neighbours, k, which means b/c > k. In this case, cooperation can evolve as a consequence of 'social viscosity' even in the absence of reputation effects or strategic complexity.

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Scale-Free Networks Provide a Unifying Framework for the Emergence of Cooperation

João F. C. Santos, J. M. Pacheco (2005)

We study the evolution of cooperation in the framework of evolutionary game theory, adopting the prisoner's dilemma and snowdrift game as metaphors of cooperation between unrelated individuals. In sharp contrast with previous results we find that, whenever individuals interact following networks of contacts generated via growth and preferential attachment, leading to strong correlations between individuals, cooperation becomes the dominating trait throughout the entire range of parameters of both games, as such providing a unifying framework for the emergence of cooperation. Such emergence is shown to be inhibited whenever the correlations between individuals are decreased or removed. These results are shown to apply from very large population sizes down to small communities with nearly 100 individuals.