Community structure benefits the fixation of cooperation under strong selection

Recent empirical studies suggest that heavy-tailed distributions of human activities are universal in real social dynamics [Muchnik, emph{et al.}, Sci. Rep. textbf{3}, 1783 (2013)]. On the other hand, community structure is ubiquitous in biological and social networks [M.~E.~J. Newman, Nat. Phys. textbf{8}, 25 (2012)]. Motivated by these facts, we here consider the evolutionary Prisoners dilemma game taking place on top of a real social network to investigate how the community structure and the heterogeneity in activity of individuals affect the evolution of cooperation. In particular, we account for a variation of the birth-death process (which can also be regarded as a proportional imitation rule from social point of view) for the strategy updating under both weak- and strong-selection (meaning the payoffs harvested from games contribute either slightly or heavily to the individuals performance). By implementing comparative studies, where the players are selected either randomly or in terms of their actual activities to playing games with their immediate neighbors, we figure out that heterogeneous activity benefits the emergence of collective cooperation in harsh environment (the action for cooperation is costly) under strong selection, while it impairs the formation of altruism under weak selection. Moreover, we find that the abundance of communities in the social network can evidently foster the fixation of cooperation under strong-selection, in contrast to the games evolving on the randomized counterparts. Our results are therefore helpful for us to better understand the evolution of cooperation in real social systems.

Boosting cooperation by involving extortion in spatial Prisoners dilemma

We study the evolution of cooperation in spatial Prisoners dilemma games with and without extortion by adopting aspiration-driven strategy updating rule. We focus explicitly on how the strategy updating manner (whether synchronous or asynchronous) and also the introduction of extortion strategy affect the collective outcome of the games. By means of Monte Carlo (MC) simulations as well as dynamical cluster techniques, we find that the involvement of extortioners facilitates the boom of cooperators in the population (and whom can always dominate the population if the temptation to defect is not too large) for both synchronous and asynchronous strategy updating, in stark contrast to the otherwise case, where cooperation is promoted for intermediate aspiration level with synchronous strategy updating, but is remarkably inhibited if the strategy updating is implemented asynchronously. We explain the results by configurational analysis and find that the presence of extortion leads to the checkerboard-like ordering of cooperators and extortioners, which enable cooperators to prevail in the population with both strategy updating manners. Moreover, extortion itself is evolutionary stable, and therefore acts as the incubator for the evolution of cooperation.

Social dilemma alleviated by sharing the gains with immediate neighbors

We study the evolution of cooperation in the evolutionary spatial prisoners dilemma game (PDG) and snowdrift game (SG), within which a fraction $alpha$ of the payoffs of each player gained from direct game interactions is shared equally by the immediate neighbors. The magnitude of the parameter $alpha$ therefore characterizes the degree of the relatedness among the neighboring players. By means of extensive Monte Carlo simulations as well as an extended mean-field approximation method, we trace the frequency of cooperation in the stationary state. We find that plugging into relatedness can significantly promote the evolution of cooperation in the context of both studied games. Unexpectedly, cooperation can be more readily established in the spatial PDG than that in the spatial SG, given that the degree of relatedness and the cost-to-benefit ratio of mutual cooperation are properly formulated. The relevance of our model with the stakeholder theory is also briefly discussed.

Diversity of reproduction time scale promotes cooperation in spatial prisoners dilemma games

We study an evolutionary spatial prisoners dilemma game where the fitness of the players is determined by both the payoffs from the current interaction and their history. We consider the situation where the selection timescale is slower than the interaction timescale. This is done by implementing probabilistic reproduction on an individual level. We observe that both too fast and too slow reproduction rates hamper the emergence of cooperation. In other words, there exists an intermediate selection timescale that maximizes cooperation. Another factor we find to promote cooperation is a diversity of reproduction timescales.

Effects of free will and massive opinion in majority rule model

We study the effects of free will and massive opinion of multi-agents in a majority rule model wherein the competition of the two types of opinions is taken into account. To address this issue, we consider two specific models (model I and model II) involving different opinion-updating dynamics. During the opinion-updating process, the agents either interact with their neighbors under a majority rule with probability $1-q$, or make their own decisions with free will (model I) or according to the massive opinion (model II) with probability $q$. We investigate the difference of the average numbers of the two opinions as a function of $q$ in the steady state. We find that the location of the order-disorder phase transition point may be shifted according to the involved dynamics, giving rise to either smooth or harsh conditions to achieve an ordered state. For the practical case with a finite population size, we conclude that there always exists a threshold for $q$ below which a full consensus phase emerges. Our analytical estimations are in good agreement with simulation results.

Congestion diffusion and decongestion strategy in networked traffic

We study the information traffic in Barabasi-Albert scale free networks wherein each node has finite queue length to store the packets. It is found that in the case of shortest path routing strategy the networks undergo a first order phase transition i.e., from a free flow state to full congestion sate, with the increasing of the packet generation rate. We also incorporate random effect (namely random selection of a neighbor to deliver packets) as well as a control method (namely the packet-dropping strategy of the congested nodes after some delay time $T$) into the routing protocol to test the traffic capacity of the heterogeneous networks. It is shown that there exists optimal value of $T$ for the networks to achieve the best handling ability, and the presence of appropriate random effect also attributes to the performance of the networks.

Effects of inhomogeneous activity of players and noise on cooperation in spatial public goods games

We study the public goods game in the noisy case by considering the players with inhomogeneous activity teaching on a square lattice. It is shown that the introduction of the inhomogeneous activity of teaching of the players can remarkably promote cooperation. By investigating the effects of noise on cooperative behavior in detail, we find that the variation of cooperator density $rho_C$ with the noise parameter $kappa$ displays several different behaviors: $rho_C$ monotonically increases (decreases) with $kappa$; $rho_C$ firstly increases (decreases) with $kappa$ and then it decreases (increases) monotonically after reaching its maximum (minimum) value, which depends on the amount of the multiplication factor $r$, on whether the system is homogeneous or inhomogeneous, and on whether the adopted updating is synchronous or asynchronous. These results imply that the noise plays an important and nontrivial role in the evolution of cooperation.

Effects of inhomogeneous influence of individuals on an order-disorder transition in opinion dynamics

We study the effects of inhomogeneous influence of individuals on collective phenomena. We focus analytically on a typical model of the majority rule, applied to the completely connected agents. Two types of individuals $A$ and $B$ with different influence activity are introduced. The individuals $A$ and $B$ are distributed randomly with concentrations $ u$ and $1- u$ at the beginning and fixed further on. Our main result is that the location of the order-disorder transition is affected due to the introduction of the inhomogeneous influence. This result highlights the importance of inhomogeneous influence between different types of individuals during the process of opinion updating.

Cooperation enhanced by the difference between interaction and learning neighborhoods for evolutionary spatial prisoners dilemma games

We study an evolutionary prisoners dilemma game with two layered graphs, where the lower layer is the physical infrastructure on which the interactions are taking place and the upper layer represents the connections for the strategy adoption (learning) mechanism. This system is investigated by means of Monte Carlo simulations and an extended pair-approximation method. We consider the average density of cooperators in the stationary state for a fixed interaction graph, while varying the number of edges in the learning graph. According to the Monte Carlo simulations, the cooperation is modified substantially in a way resembling a coherence-resonance-like behavior when the number of learning edges is increased. This behavior is reproduced by the analytical results.