Cooperation with both synergistic and local interactions can be worse than each alone

Cooperation is ubiquitous ranging from multicellular organisms to human societies. Population structures indicating individuals' limited interaction ranges are crucial to understand this issue. But it is still at large to what extend multiple interactions involving nonlinearity in payoff play a role on cooperation in structured populations. Here we show a rule, which determines the emergence and stabilization of cooperation, under multiple discounted, linear, and synergistic interactions. The rule is validated by simulations in homogenous and heterogenous structured populations. We find that the more neighbors there are the harder for cooperation to evolve for multiple interactions with linearity and discounting. For synergistic scenario, however, distinct from its pairwise counterpart, moderate number of neighbors can be the worst, indicating that synergistic interactions work with strangers but not with neighbors. Our results suggest that the combination of different factors which promotes cooperation alone can be worse than that with every single factor.Comment: 32 pages, 4 figure

High-Accuracy Approximation of Evolutionary Pairwise Games on Complex Networks

Previous studies have shown that the topological properties of a complex network, such as heterogeneity and average degree, affect the evolutionary game dynamics on it. However, traditional numerical simulations are usually time-consuming and demand a lot of computational resources. In this paper, we propose the method of dynamical approximate master equations (DAMEs) to accurately approximate the evolutionary outcomes on complex networks. We demonstrate that the accuracy of DAMEs supersedes previous standard pairwise approximation methods, and DAMEs require far fewer computational resources than traditional numerical simulations. We use prisoner's dilemma and snowdrift game on regular and scale-free networks to demonstrate the applicability of DAMEs. Overall, our method facilitates the investigation of evolutionary dynamics on a broad range of complex networks, and provides new insights into the puzzle of cooperation.Comment: 21 pages, 4 figure

Temporal higher-order interactions facilitate the evolution of cooperation

Motivated by the vital progress of modeling higher-order interactions by hypernetworks, where a link connects more than two individuals, we study the evolution of cooperation on temporal hypernetworks. We find that temporal hypernetworks may promote cooperation compared with their static counterparts. Our results offer new insights into the impact of network temporality in higher-order interactions on understanding the evolution of cooperation, suggesting traditional networks based on pairwise or static interactions may underestimate the potential of local interactions to foster cooperation.Comment: 6 pages, 4 figure

Imitation dynamics on networks with incomplete social information

Imitation is an important social learning heuristic in animal and human societies that drives the evolution of collective behaviors. Previous explorations find that the fate of cooperators has a sensitive dependence on the protocol of imitation, including the number of social peers used for comparison and whether one's own performance is considered. This leads to a puzzle about how to quantify the impact of different styles of imitation on the evolution of cooperation. Here, we take a novel perspective on the personal and social information required by imitation. We develop a general model of imitation dynamics with incomplete social information, which unifies classical imitation processes including death-birth and pairwise-comparison update rules. In pairwise social dilemmas, we find that cooperation is most easily promoted if individuals neglect personal information when imitating. If personal information is considered, cooperators evolve more readily with more social information. Intriguingly, when interactions take place in larger groups on networks with low degrees of clustering, using more personal and less social information better facilitates cooperation. We offer a unifying perspective uncovering intuition behind these phenomena by examining the rate and range of competition induced by different social dilemmas.Comment: 14pages, 5 figure

Interactive diversity promotes the evolution of cooperation in structured populations

Evolutionary games on networks traditionally assume that each individual adopts an identical strategy to interact with all its neighbors in each generation. Considering the prevalent diversity of individual interactions in the real society, here we propose the concept of interactive diversity, which allows individuals to adopt different strategies against different neighbors in each generation. We investigate the evolution of cooperation based on the edge dynamics rather than the traditional nodal dynamics in networked systems. The results show that, without invoking any other mechanisms, interactive diversity drives the frequency of cooperation to a high level for a wide range of parameters in both well-mixed and structured populations. Even in highly connected populations, cooperation still thrives. When interactive diversity and large topological heterogeneity are combined together, however, in the relaxed social dilemma, cooperation level is lower than that with just one of them, implying that the combination of many promotive factors may make a worse outcome. By an analytical approximation, we get the condition under which interactive diversity provides more advantages for cooperation than traditional evolutionary dynamics does. Numerical simulations validating the approximation are also presented. Our work provides a new line to explore the latent relation between the ubiquitous cooperation and individuals' distinct responses in different interactions. The presented results suggest that interactive diversity should receive more attention in pursuing mechanisms fostering cooperation.National Natural Science Foundation (China) (Grants 61375120 and 61533001).China Scholarship Council (201406010195