The environment has a strong influence on a population's evolutionary dynamics. Driven by both intrinsic and external factors, the environment is subject to continuous change in nature. To model an ever-changing environment, we develop a framework of evolutionary dynamics with stochastic game transitions, where individuals' behaviors together with the games they play in one time step decide the games to be played next time step. Within this framework , we study the evolution of cooperation in structured populations and find a simple rule: natural selection favors cooperation over defection if the ratio of the benefit provided by an altruistic behavior, b, to the corresponding cost, c, exceeds k-k', which means b/c>k-k', where k is the average number of neighbors  and k' captures the effects from game transitions. We show that even if each individual game opposes cooperation , allowing for a transition between them can result in a favorable outcome for cooperation. Even small variations in different games being played can promote cooperation markedly. Our work suggests that interdependence between the environment and the individuals' behaviors may explain the large-scale cooperation in realistic systems even when cooperation is expensive relative to its benefit .
The environment has a strong influence on a population's evolutionary dynamics. Driven by both intrinsic and external factors, the environment is subject to continual change in nature. To capture an ever-changing environment, we consider a model of evolutionary dynamics with game transitions, where individuals' behaviors together with the games they play in one time step influence the games to be played next time step. Within this model , we study the evolution of cooperation in structured populations and find a simple rule: weak selection favors cooperation over defection if the ratio of the benefit provided by an altruistic behavior, b, to the corresponding cost, c, exceeds k-k', where k is the average number of neighbors of an individual and k' captures the effects of the game transitions. Even if cooperation cannot be favored in each individual game , allowing for a transition to a relatively valuable game after mutual cooperation and to a less valuable game after defection can result in a favorable outcome for cooperation. In particular, small variations in different games being played can promote cooperation markedly. Our results suggest that simple game transitions can serve as a mechanism for supporting prosocial behaviors in highly-connected populations .
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develop a framework
consider a model
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stochastic
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natural
weak
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which means b/c>k-k',
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of an individual
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between them
to a relatively valuable game after mutual cooperation and to a less valuable game after defection
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work suggests that interdependence between the environment and the individuals' behaviors may explain the large-scale cooperation in realistic systems even when cooperation is expensive relative to its benefit
results suggest that simple game transitions can serve as a mechanism for supporting prosocial behaviors in highly-connected populations