Effects of strategy-migration direction and noise in the evolutionary spatial prisoner's dilemma

Spatial games are crucial for understanding patterns of cooperation in nature (and to some extent society). They are known to be more sensitive to local symmetries than e.g. spin models. This paper concerns the evolution of the prisoner's dilemma game on regular lattices with three different types of neighborhoods -- the von Neumann-, Moore-, and kagome types. We investigate two kinds of dynamics for the players to update their strategies (that can be unconditional cooperator or defector). Depending on the payoff difference, an individual can adopt the strategy of a random neighbor (a voter-model-like dynamics, VMLD), or impose its strategy on a random neighbor, i.e., invasion-like dynamics (IPLD). In particular, we focus on the effects of noise, in combination with the strategy dynamics, on the evolution of cooperation. We find that VMLD, compared to IPLD, better supports the spreading and sustaining of cooperation. We see that noise has nontrivial effects on the evolution of cooperation: maximum cooperation density can be realized either at a medium noise level, in the limit of zero noise, or in both these regions. The temptation to defect and the local interaction structure determine the outcome. Especially, in the low noise limit, the local interaction plays a crucial role in determining the fate of cooperators. We elucidate these both by numerical simulations and mean-field cluster approximation methods.Comment: 9 pages, 9 figure

Modeling scientific-citation patterns and other triangle-rich acyclic networks

We propose a model of the evolution of the networks of scientific citations. The model takes an out-degree distribution (distribution of number of citations) and two parameters as input. The parameters capture the two main ingredients of the model, the aging of the relevance of papers and the formation of triangles when new papers cite old. We compare our model with three network structural quantities of an empirical citation network. We find that an unique point in parameter space optimizing the match between the real and model data for all quantities. The optimal parameter values suggest that the impact of scientific papers, at least in the empirical data set we model is proportional to the inverse of the number of papers since they were published.Comment: 4 pages, 4 figure

Boosting cooperation by involving extortion in spatial Prisoner's dilemma

We study the evolution of cooperation in spatial Prisoner's 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.Comment: 7 pages, 4 figures, all comments are welcome

Social dilemma alleviated by sharing the gains with immediate neighbors

We study the evolution of cooperation in the evolutionary spatial prisoner's 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.Comment: 9 pages, 4 figure

Diversity of reproduction time scale promotes cooperation in spatial prisoner's dilemma games

We study an evolutionary spatial prisoner's 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.Comment: 7 pages, 8 figure

Message spreading in networks with stickiness and persistence: Large clustering does not always facilitate large-scale diffusion

Recent empirical studies have confirmed the key roles of complex contagion mechanisms such as memory, social reinforcement, and decay effects in information diffusion and behaviour spreading. Inspired by this fact, we here propose a new agent--based model to capture the whole picture of the joint action of the three mechanisms in information spreading, by quantifying the complex contagion mechanisms as stickiness and persistence, and carry out extensive simulations of the model on various networks. By numerical simulations as well as theoretical analysis, we find that the stickiness of the message determines the critical dynamics of message diffusion on tree-like networks, whereas the persistence plays a decisive role on dense regular lattices. In either network, the greater persistence can effectively make the message more invasive. Of particular interest is that our research results renew our previous knowledge that messages can spread broader in networks with large clustering, which turns out to be only true when they can inform a non-zero fraction of the population in the limit of large system size.Comment: 12pages, 7 figures, Supporting Information (20 pages), accepted by Sci. Re

Small world yields optimal public goods in presence of both altruistic and selfish cooperators

Empirical studies have shown that individuals' behaviors are largely influenced by social conformity, including punishment. However, a coevolutionary theoretical framework that takes into account effects of conformity on individuals' punishment behaviors has not been put forward yet. Herein we propose a coevolutionary game model to extend the theory of cooperation with conformity in spatial public goods game by considering pool punishment, as well as two converse feedback modes of conformity that strongly affect cooperators' punishment behaviors. We focus on how different parameters and spatial structures govern evolutionary dynamics on three different kinds of networks by employing mean-field analysis based on replicator dynamics and Monte Carlo simulations. On regular lattices, defectors are overall extincted since cooperators, especially selfish cooperators, have great evolutionary advantages due to strong network reciprocity, and at the same time the number of altruistic cooperators decays. Conversely, abundant shortcuts in regular random networks lead to the prevalence of altruistic cooperators, but cooperators suffer from free-riding behaviors of defectors. Of particular interest, we find that small-world topology can simultaneously help cooperators successfully outperform defectors by means of strong network reciprocity, and enable rich contacting opportunities with defectors to facilitate the expansion of altruistic cooperators. Therefore, we clarify that small world is the optimal topology subject to the dominance of altruistic cooperators.Comment: 12 pages 14 figure

Kuramoto dilemma alleviated by optimizing connectivity and rationality

Recently, Antonioni and Cardillo proposed a coevolutionary model based on the intertwining of oscillator synchronization and evolutionary game theory [Phys. Rev. Lett. \textbf{118}, 238301 (2017)], in which each Kuramoto oscillator can decide whether to interact-or not-with its neighbors, and all oscillators can receive some benefits from the local synchronization but those who choose to interact must pay a cost. Oscillators are allowed to update their strategies according to payoff difference, wherein the strategy of an oscillator who has obtained higher payoff is more likely to be followed. Utilizing this coevolutionary model, we find that the global synchronization level reaches the highest level when the average degree of the underlying interaction network is moderate. We also study how synchronization is affected by the individual rationality in choosing strategy

Behavior of susceptible-vaccinated--infected--recovered epidemics with diversity in the infection rate of the individuals

We study a susceptible-vaccinated--infected--recovered (SVIR) epidemic-spreading model with diversity of infection rate of the individuals. By means of analytical arguments as well as extensive computer simulations, we demonstrate that the heterogeneity in infection rate can either impede or accelerate the epidemic spreading, which depends on the amount of vaccinated individuals introduced in the population as well as the contact pattern among the individuals. Remarkably, as long as the individuals with different capability of acquiring the disease interact with unequal frequency, there always exist a cross point for the fraction of vaccinated, below which the diversity of infection rate hinders the epidemic spreading and above which expedites it. The overall results are robust to the SVIR dynamics defined on different population models; the possible applications of the results are discussed.Comment: 9 pages, many figure

Does the scale-free topology favor the emergence of cooperation?

In a recent Letter [F.C. Santos and J. M. Pacheco Phys. Rev. Lett. \textbf{95}, 098104 (2005)], the scale-free networks are found to be advantageous for the emergence of cooperation. In the present work an evolutionary prisoner's dilemma game with players located on Barab\'asi-Albert scale-free networks is studied in detail. The players are pure strategist and can follow two strategies: either to defect or to cooperate. Serval alternative update rules determining the evolution of each player's strategy are considered. Using systematic Monte Carlo simulations we have calculated the average density of cooperators as a function of the temptation to defect. It is shown that the results obtained by numerical experiments depend strongly on the dynamics of the game, which could lower the important of scale-free topology on the persistence of the cooperation. Particularly, the system exhibits a phase transition, from active state (coexistence of cooperators and defectors) to absorbing state (only defectors surviving) when allowing `` worse\rq\rq strategy to be imitated in the evolution of the game.Comment: 4 pages, 4 figures. some language mistakes are corrected and a new figure is provide