Evolutionary dynamics of cooperation on interdependent networks with Prisoner's Dilemma and Snowdrift Game

The world in which we are living is a huge network of networks and should be described by interdependent networks. The interdependence between networks significantly affects the evolutionary dynamics of cooperation on them. Meanwhile, due to the diversity and complexity of social and biological systems, players on different networks may not interact with each other by the same way, which should be described by multiple models in evolutionary game theory, such as the Prisoner's Dilemma and Snowdrift Game. We therefore study the evolutionary dynamics of cooperation on two interdependent networks playing different games respectively. We clearly evidence that, with the increment of network interdependence, the evolution of cooperation is dramatically promoted on the network playing Prisoner's Dilemma. The cooperation level of the network playing Snowdrift Game reduces correspondingly, although it is almost invisible. In particular, there exists an optimal intermediate region of network interdependence maximizing the growth rate of the evolution of cooperation on the network playing Prisoner's Dilemma. Remarkably, players contacting with other network have advantage in the evolution of cooperation than the others on the same network.Comment: 6 pages, 6 figure

Conformity Hinders the Evolution of Cooperation on Scale-Free Networks

We study the effects of conformity, the tendency of humans to imitate locally common behaviors, in the evolution of cooperation when individuals occupy the vertices of a graph and engage in the one-shot Prisoner's Dilemma or the Snowdrift game with their neighbors. Two different graphs are studied: rings (one-dimensional lattices with cyclic boundary conditions) and scale-free networks of the Barabasi-Albert type. The proposed evolutionary-graph model is studied both by means of Monte Carlo simulations and an extended pair-approximation technique. We find improved levels of cooperation when evolution is carried on rings and individuals imitate according to both the traditional pay-off bias and a conformist bias. More important, we show that scale-free networks are no longer powerful amplifiers of cooperation when fair amounts of conformity are introduced in the imitation rules of the players. Such weakening of the cooperation-promoting abilities of scale-free networks is the result of a less biased flow of information in scale-free topologies, making hubs more susceptible of being influenced by less-connected neighbors.Comment: 14 pages, 11 figure

Degree Variance and Emotional Strategies Catalyze Cooperation in Dynamic Signed Networks

We study the problem of the emergence of cooperation in dynamic signed networks where agent strategies coevolve with relational signs and network topology. Running simulations based on an agent-based model, we compare results obtained in a regular lattice initialization with those obtained on a comparable random network initialization. We show that the increased degree heterogeneity at the outset enlarges the parametric conditions in which cooperation survives in the long run. Furthermore, we show how the presence of sign-dependent emotional strategies catalyze the evolution of cooperation with both network topology initializations.Comment: 16 Pages, Proceeding of the European Conference on Modelling and Simumatio

Social dilemmas in an online social network: the structure and evolution of cooperation

We investigate two paradigms for studying the evolution of cooperation--Prisoner's Dilemma and Snowdrift game in an online friendship network obtained from a social networking site. We demonstrate that such social network has small-world property and degree distribution has a power-law tail. Besides, it has hierarchical organizations and exhibits disassortative mixing pattern. We study the evolutionary version of the two types of games on it. It is found that enhancement and sustainment of cooperative behaviors are attributable to the underlying network topological organization. It is also shown that cooperators can survive when confronted with the invasion of defectors throughout the entire ranges of parameters of both games. The evolution of cooperation on empirical networks is influenced by various network effects in a combined manner, compared with that on model networks. Our results can help understand the cooperative behaviors in human groups and society.Comment: 14 pages, 7 figure

Evolution of ethnocentrism on undirected and directed Barabási-Albert networks

Using Monte Carlo simulations, we study the evolution of contigent cooperation and ethnocentrism in the one-move game. Interactions and reproduction among computational agents are simulated on undirected and directed Barabási-\ud Albert (BA) networks. We first replicate the Hammond-Axelrod model of in-group favoritism on a square lattice and then generalize this model on undirected and directed BA networks for both asexual and sexual reproduction cases. Our simulations demonstrate that irrespective of the mode of reproduction, ethnocentric strategy becomes common even though cooperation is individually costly and mechanisms such as reciprocity or conformity are absent. Moreover, our results indicate that the spread of favoritism toward similar others highly depends on the network topology and the associated heterogeneity of the studied population

A condition of cooperation. Games on network

Natural selection is often regarded as a result of severe competition. Defect seems beneficial for a single individual in many cases.However, cooperation is observed in many levels of biological systems ranging from single cells to animals, including human society. We have yet known that in unstructured populations, evolution favors defectors over cooperators. On the other hand, there have been much interest on evolutionary games^1,2^ on structured population and on graphs^3-16^. Structures of biological systems and societies of animals can be taken as networks. They discover that network structures determine results of the games. Together with the recent interest of complex networks^17,18^, many researchers investigate real network structures. Recently even economists study firms' transactions structure^19^. Seminal work^11^ derives the condition of favoring cooperation for evolutionary games on networks, that is, benefit divided by cost, _b/c_, exceeds average degree, (_k_). Although this condition has been believed so far^20^, we find the condition is _b/c_ (_k~nm~_) instead. _k~nm~_ is the mean nearest neighbor degree. Our condition enables us to compare how network structure enhances cooperation across different kinds of networks. Regular network favors most, scale free network least. On ideal scale free networks, cooperation is unfeasible. We could say that (_k_) is the degree of itself, while _k~nm~_ is that of others. One of the most interesting points in network theory is that results depend not only on itself but also on others. In evolutionary games on network, we find the same characteristic