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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 , cooperators pervade into the whole population in the inverse sigmoidally and linearly dependent pattern, while loners completely dominate in the sigmoidally pattern, when defectors abound at the starting point. In the other typical cases, cooperators uniformly take over the whole population, though sometimes the evolutionary processes are different. Parameters , . Upper row , middle row , and low row .
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pone-0063801-g004: 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 , cooperators pervade into the whole population in the inverse sigmoidally and linearly dependent pattern, while loners completely dominate in the sigmoidally pattern, when defectors abound at the starting point. In the other typical cases, cooperators uniformly take over the whole population, though sometimes the evolutionary processes are different. Parameters , . Upper row , middle row , and low row .

Mentions: As rises to the moderate level, the cycle still does not exist, while cooperators have more chances to establish (Figure 3). Irrespective of the risk removal pattern, loners take over the whole population if defectors account for the overwhelming majority at the outset of the evolution (Figure 3B, 3F, 3J). Depending on the risk removal patterns, the population exhibits rich dynamics. Of the remaining three starting mixes, cooperators and defectors always coexist under the sigmoidal pattern (Figure 3I, 3K, 3L) while cooperators evolve to be the only survivors in the inverse sigmoidally pattern (Figure 3A, 3C, 3D). However, loners win out after a transiently cyclical dominance for the population starting with equal fractions under the linear pattern (Figure 3H). This also implies that the fixed point is unstable. The population starting from this point would oscillate around it with the amplitude increasing. Until eventually, loners homogenize the population. With arriving at , cooperation stands conspicuously advantageous as the evolution most of the time ends up with the triumph of cooperators (Figure 4), apart from that loners occasionally directly spread into the whole population after beating the prevalent defectors in the sigmoidal pattern (Figure 4F, 4J).


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 , cooperators pervade into the whole population in the inverse sigmoidally and linearly dependent pattern, while loners completely dominate in the sigmoidally pattern, when defectors abound at the starting point. In the other typical cases, cooperators uniformly take over the whole population, though sometimes the evolutionary processes are different. Parameters , . Upper row , middle row , and low row .
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3672156&req=5

pone-0063801-g004: 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 , cooperators pervade into the whole population in the inverse sigmoidally and linearly dependent pattern, while loners completely dominate in the sigmoidally pattern, when defectors abound at the starting point. In the other typical cases, cooperators uniformly take over the whole population, though sometimes the evolutionary processes are different. Parameters , . Upper row , middle row , and low row .
Mentions: As rises to the moderate level, the cycle still does not exist, while cooperators have more chances to establish (Figure 3). Irrespective of the risk removal pattern, loners take over the whole population if defectors account for the overwhelming majority at the outset of the evolution (Figure 3B, 3F, 3J). Depending on the risk removal patterns, the population exhibits rich dynamics. Of the remaining three starting mixes, cooperators and defectors always coexist under the sigmoidal pattern (Figure 3I, 3K, 3L) while cooperators evolve to be the only survivors in the inverse sigmoidally pattern (Figure 3A, 3C, 3D). However, loners win out after a transiently cyclical dominance for the population starting with equal fractions under the linear pattern (Figure 3H). This also implies that the fixed point is unstable. The population starting from this point would oscillate around it with the amplitude increasing. Until eventually, loners homogenize the population. With arriving at , cooperation stands conspicuously advantageous as the evolution most of the time ends up with the triumph of cooperators (Figure 4), apart from that loners occasionally directly spread into the whole population after beating the prevalent defectors in the sigmoidal pattern (Figure 4F, 4J).

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