scholarly journals Invasion of Cooperation in Scale-Free Networks: Accumulated versus Average Payoffs

2017 ◽  
Vol 23 (1) ◽  
pp. 25-33 ◽  
Author(s):  
Genki Ichinose ◽  
Hiroki Sayama
Keyword(s):  
Evolutionary Dynamics ◽  
Evolutionarily Stable Strategy ◽  
Average Degree ◽  
Structured Populations ◽  
Evolution Of Cooperation ◽  
Scale Free ◽  
Invasion Mechanism ◽  
Cooperative Strategies ◽  
Average Payoff ◽  
Scale Free Networks

It is well known that cooperation cannot be an evolutionarily stable strategy for a non-iterative game in a well-mixed population. In contrast, structured populations favor cooperation, since cooperators can benefit each other by forming local clusters. Previous studies have shown that scale-free networks strongly promote cooperation. However, little is known about the invasion mechanism of cooperation in scale-free networks. To study microscopic and macroscopic behaviors of cooperators' invasion, we conducted computational experiments on the evolution of cooperation in scale-free networks where, starting from all defectors, cooperators can spontaneously emerge by mutation. Since the evolutionary dynamics are influenced by the definition of fitness, we tested two commonly adopted fitness functions: accumulated payoff and average payoff. Simulation results show that cooperation is strongly enhanced with the accumulated payoff fitness compared to the average payoff fitness. However, the difference between the two functions decreases as the average degree increases. As the average degree increases, cooperation decreases for the accumulated payoff fitness, while it increases for the average payoff fitness. Moreover, for the average payoff fitness, low-degree nodes play a more important role in spreading cooperative strategies than for the accumulated payoff fitness.

scholarly journals Parent-preferred dispersal promotes cooperation in structured populations

2019 ◽  
Vol 286 (1895) ◽  
pp. 20181949 ◽  
Author(s):  
Xiaojie Chen ◽  
Åke Brännström ◽  
Ulf Dieckmann
Keyword(s):  
Pairwise Comparison ◽  
Small World ◽  
Structured Populations ◽  
Evolution Of Cooperation ◽  
Pair Approximation ◽  
Scale Free ◽  
Scale Free Networks ◽  
Different Types ◽  
Population Structures ◽  
Update Rules

Dispersal is a key process for the emergence of social and biological behaviours. Yet, little attention has been paid to dispersal's effects on the evolution of cooperative behaviour in structured populations. To address this issue, we propose two new dispersal modes, parent-preferred and offspring-preferred dispersal, incorporate them into the birth–death update rule, and consider the resultant strategy evolution in the prisoner's dilemma on random-regular, small-world, and scale-free networks, respectively. We find that parent-preferred dispersal favours the evolution of cooperation in these different types of population structures, while offspring-preferred dispersal inhibits the evolution of cooperation in homogeneous populations. On scale-free networks when the strength of parent-preferred dispersal is weak, cooperation can be enhanced at intermediate strengths of offspring-preferred dispersal, and cooperators can coexist with defectors at high strengths of offspring-preferred dispersal. Moreover, our theoretical analysis based on the pair-approximation method corroborates the evolutionary outcomes on random-regular networks. We also incorporate the two new dispersal modes into three other update rules (death-birth, imitation, and pairwise comparison updating), and find that similar results about the effects of parent-preferred and offspring-preferred dispersal can again be observed in the aforementioned different types of population structures. Our work, thus, unveils robust effects of preferential dispersal modes on the evolution of cooperation in different interactive environments.

The analysis of evolutionary prisoner’s dilemma game based on weighting effect

2021 ◽  
pp. 2150066
Author(s):  
Xinting Hu ◽  
Mengyun Wu
Keyword(s):  
Prisoner's Dilemma ◽  
Weighting Function ◽  
Random Network ◽  
Cooperative Behavior ◽  
Equilibrium Points ◽  
Prisoner’S Dilemma ◽  
The Real ◽  
Scale Free ◽  
Cooperative Strategies ◽  
Average Payoff

In this paper, an improved evolutionary prisoner’s dilemma (PD) game model is proposed by considering the weighting effect. Taking into account individual’s perceived payoff (benefits), the evolutionary tendency of the cooperators and three equilibrium points of the proposed model are obtained. We then numerically investigate how different exterior and interior factors influence on individuals’ cooperative behavior and their payoff both in the ER random network and the BA scale-free network. Our results reveal that the heterogeneous network structure is conducive to cooperation. In addition, the existence of leader nodes is an important driving force for promoting individuals’ cooperation. By further analyzing the rationality coefficient which appears in the weighting function, we obtain that a greater of irrationality could lead more people to take cooperative strategies. Finally, two indicators which are used to measure the real average payoff and perceived average payoff are defined. The results show that the real average payoff and perceived average payoff are larger in the heterogeneity network than that in homogeneous network.

Punishment Leads to Cooperative Behavior in Structured Societies

2012 ◽  
Vol 20 (2) ◽  
pp. 301-319 ◽  
Author(s):  
Shade T. Shutters
Keyword(s):  
Social Structure ◽  
Computer Simulations ◽  
Degree Distribution ◽  
Cooperative Behavior ◽  
Evolution Of Cooperation ◽  
Scale Free ◽  
Structured Population ◽  
Altruistic Punishment ◽  
Costly Punishment ◽  
Scale Free Networks

Altruistic punishment occurs when an agent incurs a cost to punish another but receives no material benefit for doing so. Despite the seeming irrationality of such behavior, humans in laboratory settings routinely pay to punish others even in anonymous, one-shot settings. Costly punishment is ubiquitous among social organisms in general and is increasingly accepted as a mechanism for the evolution of cooperation. Yet if it is true that punishment explains cooperation, the evolution of altruistic punishment remains a mystery. In a series of computer simulations I give agents the ability to punish one another while playing a continuous prisoner's dilemma. In simulations without social structure, expected behavior evolves—agents do not punish and consequently no cooperation evolves. Likewise, in simulations with social structure but no ability to punish, no cooperation evolves. However, in simulations where agents are both embedded in a social structure and have the option to inflict costly punishment, cooperation evolves quite readily. This suggests a simple and broadly applicable explanation of cooperation for social organisms that have nonrandom social structure and a predisposition to punish one another. Results with scale-free networks further suggest that nodal degree distribution plays an important role in determining whether cooperation will evolve in a structured population.

scholarly journals Conformity hinders the evolution of cooperation on scale-free networks

2009 ◽  
Vol 80 (1) ◽  
Author(s):  
Jorge Peña ◽  
Henri Volken ◽  
Enea Pestelacci ◽  
Marco Tomassini
Keyword(s):  
Evolution Of Cooperation ◽  
Scale Free ◽  
Scale Free Networks

The Detection Method of Network Topological Property Based on Multiple Sampling

2012 ◽  
Vol 256-259 ◽  
pp. 2396-2400
Author(s):  
Cong Huang ◽  
D G Zhang ◽  
T J Yang ◽  
H Yang
Keyword(s):  
Topological Property ◽  
Detection Method ◽  
Sampling Frequency ◽  
Average Degree ◽  
Global Networks ◽  
Scale Free ◽  
Multiple Sampling ◽  
Scale Free Networks ◽  
Sampling Probability

Recent studies have shown that subnets of scale-free networks are not scale-free, which make it difficult to extrapolate from subnet data to properties of the global networks. Here, we discuss sampling properties of Erdö–Rényi and scale-free networks, then figure out how average degree varies with sampling probability. This finding is developed to be a practical detection method based on multiple sampling. In practice, the method could not only prove global networks and randomly sampled subnets belong to the same family of probability, but also detect unknown networks by least sampling frequency.

scholarly journals COOPERATION ON SOCIAL NETWORKS AND ITS ROBUSTNESS

2012 ◽  
Vol 15 (supp01) ◽  
pp. 1250046 ◽  
Author(s):  
ALBERTO ANTONIONI ◽  
MARCO TOMASSINI
Keyword(s):  
Social Networks ◽  
Population Dynamics ◽  
Numerical Simulations ◽  
Population Model ◽  
Evolutionary Games ◽  
Computer Models ◽  
Scale Free ◽  
Average Payoff ◽  
Scale Free Networks ◽  
Update Rules

In this work we have used computer models of social-like networks to show by extensive numerical simulations that cooperation in evolutionary games can emerge and be stable on this class of networks. The amounts of cooperation reached are at least as much as in scale-free networks but here the population model is more realistic. Cooperation is robust with respect to different strategy update rules, population dynamics, and payoff computation. Only when straight average payoff is used or there is high strategy or network noise does cooperation decrease in all games and disappear in the Prisoner's Dilemma.

scholarly journals Evolutionary dynamics with game transitions

2019 ◽  
Vol 116 (51) ◽  
pp. 25398-25404 ◽  
Author(s):  
Qi Su ◽  
Alex McAvoy ◽  
Long Wang ◽  
Martin A. Nowak
Keyword(s):  
Strong Influence ◽  
Evolutionary Dynamics ◽  
Simple Game ◽  
Structured Populations ◽  
Evolution Of Cooperation ◽  
Altruistic Behavior ◽  
Weak Selection ◽  
Time Step ◽  
Mutual Cooperation ◽  
Connected Populations

The environment has a strong influence on a population’s evolutionary dynamics. Driven by both intrinsic and external factors, the environment is subject to continual change in nature. To capture an ever-changing environment, we consider a model of evolutionary dynamics with game transitions, where individuals’ behaviors together with the games that they play in one time step influence the games to be played in the next time step. Within this model, we study the evolution of cooperation in structured populations and find a simple rule: Weak selection favors cooperation over defection if the ratio of the benefit provided by an altruistic behavior, b, to the corresponding cost, c, exceedsk−k′, where k is the average number of neighbors of an individual andk′captures the effects of the game transitions. Even if cooperation cannot be favored in each individual game, allowing for a transition to a relatively valuable game after mutual cooperation and to a less valuable game after defection can result in a favorable outcome for cooperation. In particular, small variations in different games being played can promote cooperation markedly. Our results suggest that simple game transitions can serve as a mechanism for supporting prosocial behaviors in highly connected populations.

A NEW ATTACK ON SCALE-FREE NETWORKS BASED ON CASCADING FAILURES

2009 ◽  
Vol 23 (20n21) ◽  
pp. 2497-2505 ◽  
Author(s):  
KAI YU ◽  
LILI RONG ◽  
JIANWEI WANG
Keyword(s):  
Real Life ◽  
Local Information ◽  
Average Degree ◽  
Cascading Failure ◽  
Cascading Failures ◽  
Scale Free ◽  
Scale Free Networks ◽  
Key Nodes ◽  
Attack Strategy

In this paper, based on the local information about nodes, we propose a new attack strategy, considering the average degree of the node's neighboring nodes. Adopting the cascading model proposed in Chin. Phys. Lett.25(10) (2008) 3826, we investigate the effect of the new attack strategy for the robustness against cascading failures on a typical network, i.e. BA scale-free networks. Compared with two attacks on the nodes with the highest load or the lowest load, numerically we find that our presented attack is the most efficient way to destruct the BA scale-free networks in the case of α ≤ 0.6, where α is a tunable parameter and determines to the load strength of a node. In addition, we also find that the efficiency of the new attack strategy is more obvious near the parameter α = 0.5. We expect our findings to provide insights into the protection of the key nodes for real-life networks to avoid cascading-failure-induced disasters.

scholarly journals Evolution of Cooperation in the Presence of Higher-Order Interactions: From Networks to Hypergraphs

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 744
Author(s):  
Giulio Burgio ◽  
Joan T. Matamalas ◽  
Sergio Gómez ◽  
Alex Arenas
Keyword(s):  
Evolutionary Dynamics ◽  
Higher Order ◽  
Structured Populations ◽  
Evolution Of Cooperation ◽  
Mathematical Representation ◽  
Interaction Patterns ◽  
Group Interactions ◽  
Cooperative Phenomena ◽  
Structured Population ◽  
Pairwise Models

Many real systems are strongly characterized by collective cooperative phenomena whose existence and properties still need a satisfactory explanation. Coherently with their collective nature, they call for new and more accurate descriptions going beyond pairwise models, such as graphs, in which all the interactions are considered as involving only two individuals at a time. Hypergraphs respond to this need, providing a mathematical representation of a system allowing from pairs to larger groups. In this work, through the use of different hypergraphs, we study how group interactions influence the evolution of cooperation in a structured population, by analyzing the evolutionary dynamics of the public goods game. Here we show that, likewise to network reciprocity, group interactions also promote cooperation. More importantly, by means of an invasion analysis in which the conditions for a strategy to survive are studied, we show how, in heterogeneously-structured populations, reciprocity among players is expected to grow with the increasing of the order of the interactions. This is due to the heterogeneity of connections and, particularly, to the presence of individuals standing out as hubs in the population. Our analysis represents a first step towards the study of evolutionary dynamics through higher-order interactions, and gives insights into why cooperation in heterogeneous higher-order structures is enhanced. Lastly, it also gives clues about the co-existence of cooperative and non-cooperative behaviors related to the structural properties of the interaction patterns.

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