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The increased risk of joint venture promotes social cooperation.

Wu T, Fu F, Zhang Y, Wang L - PLoS ONE (2013)

Bottom Line: Existent literature mostly focuses on the traditional public goods game, in which cooperators create public wealth unconditionally and benefit all group members unbiasedly.Analytical results show that the widely replicated population dynamics of cyclical dominance of loner, cooperator and defector disappear, while most of the time loners act as savors while eventually they also disappear.Even in the later case, cooperators still hold salient superiority in number as some defectors also survive by parasitizing.

View Article: PubMed Central - PubMed

Affiliation: Center for Systems and Control, State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing, China. wute@pku.edu.cn

ABSTRACT
The joint venture of many members is common both in animal world and human society. In these public enterprizes, highly cooperative groups are more likely to while low cooperative groups are still possible but not probable to succeed. Existent literature mostly focuses on the traditional public goods game, in which cooperators create public wealth unconditionally and benefit all group members unbiasedly. We here institute a model addressing this public goods dilemma with incorporating the public resource foraging failure risk. Risk-averse individuals tend to lead a autarkic life, while risk-preferential ones tend to participate in the risky public goods game. For participants, group's success relies on its cooperativeness, with increasing contribution leading to increasing success likelihood. We introduce a function with one tunable parameter to describe the risk removal pattern and study in detail three representative classes. Analytical results show that the widely replicated population dynamics of cyclical dominance of loner, cooperator and defector disappear, while most of the time loners act as savors while eventually they also disappear. Depending on the way that group's success relies on its cooperativeness, either cooperators pervade the entire population or they coexist with defectors. Even in the later case, cooperators still hold salient superiority in number as some defectors also survive by parasitizing. The harder the joint venture succeeds, the higher level of cooperation once cooperators can win the evolutionary race. Our work may enrich the literature concerning the risky public goods games.

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Population dynamics whenever cooperators defectors, and loners compete to survive.The lines embedded with solid triangle, square, and circle represent the evolutionary trajectories of cooperators, defectors and loners, respectively. For , in both the linearly-dependent and sigmoidally-dependent patterns, the evolution share the property that when cooperators abound, it is better to defect, while defectors' prosperity puts the loners in the advantageous place forever, and thus loners take over the whole population. In the inverse sigmoidally-dependent pattern, loners do thrive ensuing the defectors' abundance. An exception emerges while the population consists of most cooperators, it drives to the full cooperative state. Loners win the evolutionary race when the population starts with a state in which cooperators and defectors, and loners have the same share. Parameters , . Upper row , middle row , and low row .
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pone-0063801-g002: Population dynamics whenever cooperators defectors, and loners compete to survive.The lines embedded with solid triangle, square, and circle represent the evolutionary trajectories of cooperators, defectors and loners, respectively. For , in both the linearly-dependent and sigmoidally-dependent patterns, the evolution share the property that when cooperators abound, it is better to defect, while defectors' prosperity puts the loners in the advantageous place forever, and thus loners take over the whole population. In the inverse sigmoidally-dependent pattern, loners do thrive ensuing the defectors' abundance. An exception emerges while the population consists of most cooperators, it drives to the full cooperative state. Loners win the evolutionary race when the population starts with a state in which cooperators and defectors, and loners have the same share. Parameters , . Upper row , middle row , and low row .

Mentions: Let us now focus on what influence the risk-averse loners exercise on the population dynamics. Figure 2 clearly illustrates the evolutionary trajectories of the population starting with four typical mixes under the three different risk removal patterns for . Each mix corresponds to a mixed state of cooperators, defectors and loners. For such small , loners pervade the whole population in most of the twelve cases. Of interest is that cooperators are still able to win the evolutionary race provided that the population starts with cooperators themselves or loners holding the absolute majority for . The rationale behind this phenomena can be intuitively comprehended. To flip the coin determines the success of groups consisting of defectors and cooperators who fail to compete with loners from the perspective of statistics. Only when several cooperators agglomerate together, such high cooperative groups with probabilities close to succeed in averting the failure risk. Cooperators from these groups are able to beat loners and defectors. Differently, the likelihood is enhanced for the cases and when the group's cooperativeness is above yet below . Consequently, interspersed defectors can more frequently exploit and therein outperform the cooperators, which occasions the prevalence of defectors following the spawning of cooperators, as do loners after defectors. Once dominating, loners establish forever, vanishing the cyclical dominance of rock-paper-scissor type.


The increased risk of joint venture promotes social cooperation.

Wu T, Fu F, Zhang Y, Wang L - PLoS ONE (2013)

Population dynamics whenever cooperators defectors, and loners compete to survive.The lines embedded with solid triangle, square, and circle represent the evolutionary trajectories of cooperators, defectors and loners, respectively. For , in both the linearly-dependent and sigmoidally-dependent patterns, the evolution share the property that when cooperators abound, it is better to defect, while defectors' prosperity puts the loners in the advantageous place forever, and thus loners take over the whole population. In the inverse sigmoidally-dependent pattern, loners do thrive ensuing the defectors' abundance. An exception emerges while the population consists of most cooperators, it drives to the full cooperative state. Loners win the evolutionary race when the population starts with a state in which cooperators and defectors, and loners have the same share. Parameters , . Upper row , middle row , and low row .
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3672156&req=5

pone-0063801-g002: Population dynamics whenever cooperators defectors, and loners compete to survive.The lines embedded with solid triangle, square, and circle represent the evolutionary trajectories of cooperators, defectors and loners, respectively. For , in both the linearly-dependent and sigmoidally-dependent patterns, the evolution share the property that when cooperators abound, it is better to defect, while defectors' prosperity puts the loners in the advantageous place forever, and thus loners take over the whole population. In the inverse sigmoidally-dependent pattern, loners do thrive ensuing the defectors' abundance. An exception emerges while the population consists of most cooperators, it drives to the full cooperative state. Loners win the evolutionary race when the population starts with a state in which cooperators and defectors, and loners have the same share. Parameters , . Upper row , middle row , and low row .
Mentions: Let us now focus on what influence the risk-averse loners exercise on the population dynamics. Figure 2 clearly illustrates the evolutionary trajectories of the population starting with four typical mixes under the three different risk removal patterns for . Each mix corresponds to a mixed state of cooperators, defectors and loners. For such small , loners pervade the whole population in most of the twelve cases. Of interest is that cooperators are still able to win the evolutionary race provided that the population starts with cooperators themselves or loners holding the absolute majority for . The rationale behind this phenomena can be intuitively comprehended. To flip the coin determines the success of groups consisting of defectors and cooperators who fail to compete with loners from the perspective of statistics. Only when several cooperators agglomerate together, such high cooperative groups with probabilities close to succeed in averting the failure risk. Cooperators from these groups are able to beat loners and defectors. Differently, the likelihood is enhanced for the cases and when the group's cooperativeness is above yet below . Consequently, interspersed defectors can more frequently exploit and therein outperform the cooperators, which occasions the prevalence of defectors following the spawning of cooperators, as do loners after defectors. Once dominating, loners establish forever, vanishing the cyclical dominance of rock-paper-scissor type.

Bottom Line: Existent literature mostly focuses on the traditional public goods game, in which cooperators create public wealth unconditionally and benefit all group members unbiasedly.Analytical results show that the widely replicated population dynamics of cyclical dominance of loner, cooperator and defector disappear, while most of the time loners act as savors while eventually they also disappear.Even in the later case, cooperators still hold salient superiority in number as some defectors also survive by parasitizing.

View Article: PubMed Central - PubMed

Affiliation: Center for Systems and Control, State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing, China. wute@pku.edu.cn

ABSTRACT
The joint venture of many members is common both in animal world and human society. In these public enterprizes, highly cooperative groups are more likely to while low cooperative groups are still possible but not probable to succeed. Existent literature mostly focuses on the traditional public goods game, in which cooperators create public wealth unconditionally and benefit all group members unbiasedly. We here institute a model addressing this public goods dilemma with incorporating the public resource foraging failure risk. Risk-averse individuals tend to lead a autarkic life, while risk-preferential ones tend to participate in the risky public goods game. For participants, group's success relies on its cooperativeness, with increasing contribution leading to increasing success likelihood. We introduce a function with one tunable parameter to describe the risk removal pattern and study in detail three representative classes. Analytical results show that the widely replicated population dynamics of cyclical dominance of loner, cooperator and defector disappear, while most of the time loners act as savors while eventually they also disappear. Depending on the way that group's success relies on its cooperativeness, either cooperators pervade the entire population or they coexist with defectors. Even in the later case, cooperators still hold salient superiority in number as some defectors also survive by parasitizing. The harder the joint venture succeeds, the higher level of cooperation once cooperators can win the evolutionary race. Our work may enrich the literature concerning the risky public goods games.

Show MeSH