Optimal interdependence between networks for the evolution of cooperation

Recent research has identified interactions between networks as crucial for the outcome of evolutionary games taking place on them. While the consensus is that interdependence does promote cooperation by means of organizational complexity and enhanced reciprocity that is out of reach on isolated networks, we here address the question just how much interdependence there should be. Intuitively, one might assume the more the better. However, we show that in fact only an intermediate density of sufficiently strong interactions between networks warrants an optimal resolution of social dilemmas. This is due to an intricate interplay between the heterogeneity that causes an asymmetric strategy flow because of the additional links between the networks, and the independent formation of cooperative patterns on each individual network. Presented results are robust to variations of the strategy updating rule, the topology of interdependent networks, and the governing social dilemma, thus suggesting a high degree of universality

Learning and coordinating in a multilayer network

We introduce a two layer network model for social coordination incorporating two relevant ingredients: a) different networks of interaction to learn and to obtain a payoff , and b) decision making processes based both on social and strategic motivations. Two populations of agents are distributed in two layers with intralayer learning processes and playing interlayer a coordination game. We find that the skepticism about the wisdom of crowd and the local connectivity are the driving forces to accomplish full coordination of the two populations, while polarized coordinated layers are only possible for all-to-all interactions. Local interactions also allow for full coordination in the socially efficient Pareto-dominant strategy in spite of being the riskier one

Conformity enhances network reciprocity in evolutionary social dilemmas

The pursuit of highest payoffs in evolutionary social dilemmas is risky and sometimes inferior to conformity. Choosing the most common strategy within the interaction range is safer because it ensures that the payoff of an individual will not be much lower than average. Herding instincts and crowd behavior in humans and social animals also compel to conformity on their own right. Motivated by these facts, we here study the impact of conformity on the evolution of cooperation in social dilemmas. We show that an appropriate fraction of conformists within the population introduces an effective surface tension around cooperative clusters and ensures smooth interfaces between different strategy domains. Payoff-driven players brake the symmetry in favor of cooperation and enable an expansion of clusters past the boundaries imposed by traditional network reciprocity. This mechanism works even under the most testing conditions, and it is robust against variations of the interaction network as long as degree-normalized payoffs are applied. Conformity may thus be beneficial for the resolution of social dilemmas.Comment: 8 two-column pages, 5 figures; accepted for publication in Journal of the Royal Society Interfac

Spillover modes in multiplex games: double-edged effects on cooperation, and their coevolution

In recent years, there has been growing interest in studying games on multiplex networks that account for interactions across linked social contexts. However, little is known about how potential cross-context interference, or spillover, of individual behavioural strategy impact overall cooperation. We consider three plausible spillover modes, quantifying and comparing their effects on the evolution of cooperation. In our model, social interactions take place on two network layers: one represents repeated interactions with close neighbours in a lattice, the other represents one-shot interactions with random individuals across the same population. Spillover can occur during the social learning process with accidental cross-layer strategy transfer, or during social interactions with errors in implementation due to contextual interference. Our analytical results, using extended pair approximation, are in good agreement with extensive simulations. We find double-edged effects of spillover on cooperation: increasing the intensity of spillover can promote cooperation provided cooperation is favoured in one layer, but too much spillover is detrimental. We also discover a bistability phenomenon of cooperation: spillover hinders or promotes cooperation depending on initial frequencies of cooperation in each layer. Furthermore, comparing strategy combinations that emerge in each spillover mode provides a good indication of their co-evolutionary dynamics with cooperation. Our results make testable predictions that inspire future research, and sheds light on human cooperation across social domains and their interference with one another

Collaboration Conundrum: Synchrony-Cooperation Trade-off

In large groups, every collaborative act requires balancing two pressures: the need to achieve behavioural synchrony and the need to keep free riding to a minimum. This paper introduces a model of collaboration that requires both synchronisation on a social network and costly cooperation. The results show that coordination slows, and cooperativeness increases with the social network`s local integratedness, measured by the clustering coefficient. That is, in a large-group collaboration, achieving behavioural synchrony and strategic cooperation are in opposition to each other. The optimal clustering coefficient has no natural state in our species, and is determined by the ecological environment, the group`s technology set, and the group`s size. This opens the space for social technologies that solve this optimisation problem by generating optimal social network structures.Comment: 21 pages, 7 figure

Spreading processes in Multilayer Networks

Several systems can be modeled as sets of interconnected networks or networks with multiple types of connections, here generally called multilayer networks. Spreading processes such as information propagation among users of an online social networks, or the diffusion of pathogens among individuals through their contact network, are fundamental phenomena occurring in these networks. However, while information diffusion in single networks has received considerable attention from various disciplines for over a decade, spreading processes in multilayer networks is still a young research area presenting many challenging research issues. In this paper we review the main models, results and applications of multilayer spreading processes and discuss some promising research directions.Comment: 21 pages, 3 figures, 4 table

The use of multilayer network analysis in animal behaviour

Network analysis has driven key developments in research on animal behaviour by providing quantitative methods to study the social structures of animal groups and populations. A recent formalism, known as \emph{multilayer network analysis}, has advanced the study of multifaceted networked systems in many disciplines. It offers novel ways to study and quantify animal behaviour as connected 'layers' of interactions. In this article, we review common questions in animal behaviour that can be studied using a multilayer approach, and we link these questions to specific analyses. We outline the types of behavioural data and questions that may be suitable to study using multilayer network analysis. We detail several multilayer methods, which can provide new insights into questions about animal sociality at individual, group, population, and evolutionary levels of organisation. We give examples for how to implement multilayer methods to demonstrate how taking a multilayer approach can alter inferences about social structure and the positions of individuals within such a structure. Finally, we discuss caveats to undertaking multilayer network analysis in the study of animal social networks, and we call attention to methodological challenges for the application of these approaches. Our aim is to instigate the study of new questions about animal sociality using the new toolbox of multilayer network analysis.Comment: Thoroughly revised; title changed slightl

Evolutionary origin of asymptotically stable consensus

Consensus is widely observed in nature as well as in society. Up to now, many works have focused on what kind of (and how) isolated single structures lead to consensus, while the dynamics of consensus in interdependent populations remains unclear, although interactive structures are everywhere. For such consensus in interdependent populations, we refer that the fraction of population adopting a specified strategy is the same across different interactive structures. A two-strategy game as a conflict is adopted to explore how natural selection affects the consensus in such interdependent populations. It is shown that when selection is absent, all the consensus states are stable, but none are evolutionarily stable. In other words, the final consensus state can go back and forth from one to another. When selection is present, there is only a small number of stable consensus state which are evolutionarily stable. Our study highlights the importance of evolution on stabilizing consensus in interdependent populations