The role of dynamical topologies in the evolution of cooperation has received considerable attention, as some studies have demonstrated that dynamical networks are much better than static networks in terms of boosting cooperation. Here we study a dynamical model of evolution of cooperation on stochastic dynamical networks in which there are no permanent partners to each agent. Whenever a new link is created, its duration is randomly assigned without any bias or preference. We allow the agent to adaptively adjust the duration of each link during the evolution in accordance with the feedback from game interactions. By Monte Carlo simulations, we find that cooperation can be remarkably promoted by this adaptive dynamical linking mechanism both for the game of pairwise interactions, such as the Prisoner's Dilemma game (PDG), and for the game of group interactions, illustrated by the public goods game (PGG). And the faster the adjusting rate, the more successful the evolution of cooperation. We also show that in this context weak selection favors cooperation much more than strong selection does. What is particularly meaningful is that the prosperity of cooperation in this study indicates that the rationality and selfishness of a single agent in adjusting social ties can lead to the progress of altruism of the whole population.

Most previous studies concerning linking dynamics often assumed that links pairing individuals should be identified and treated differently during topology adjusting procedure, in order to promote cooperation. A common assumption was that cooperators were expected to avoid being exploited by quickly breaking up relationships with defectors. Then the so-called prosocial links linking two cooperators (abbreviated as CC links hereafter) would be much favored by evolution, whereby cooperation was promoted. However, we suggest that this is not always necessary. Here, we developed a minimal model in which an aspiration-based partner switching mechanism was embedded to regulate the evolution of cooperation in social dilemmas. Individuals adjusted social ties in a self-questioning manner in line with the learning theory. Less game information was involved during dynamic linking and all links were tackled anonymously irrespective of their types (i.e., CD links, DD links, or CC links). The main results indicate that cooperation flourishes for a broad range of parameters. The denser the underlying network, the more difficult the evolution of cooperation. More importantly, moderate aspirations do much better in promoting the evolution of altruistic behavior and for most cases there exists the optimal aspiration level that most benefits cooperation. Too strong or too weak selection intensity turns out to be pretty conducive to the evolution of cooperation in such a dynamical system.

No abstract

Real networks are not only multi-layered yet also dynamic. The role of coordinated network evolution regarding dynamic multi-layer networks where both network and strategy evolution simultaneously show diverse interdependence by layers remains poorly addressed. Here, we propose a general and simple coevolution framework to analyze how coordination of different dynamical processes affects strategy propagation in synergistically evolving interdependent networks. The strategic feedback constitutes the main driving force of network evolution yet the inherent cross-layer self-optimization functions as its compensation. We show that these two ingredients often catalyze a better performance of network evolution in propagating cooperation. Coordinated network evolution may be a doubleedged sword to cooperation and the network-adapting rate plays a crucial role in flipping its doublesided effect. It often economizes the cost and time consumption for driving the system to the full cooperation phase. Importantly, strongly coupled slow-tuned networks can outperform weakly coupled fast-regulated networks in solving social dilemmas, highlighting the fundamental advantages of coordinated network evolution and the importance of synergistic effect of dynamical processes in upholding human cooperation in multiplex networks.

No abstract