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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 only cooperators and defectors compete to survive.The intersection of  with horizontal line  (dashed line) represents the values of fraction of cooperators  (if  exists) at which payoff of cooperators is equivalent to that of defectors, i.e., .  Group's success is inverse-sigmoidally dependent on the cooperativeness of the group.  Group's success is linearly dependent on the cooperativeness of the group. In these two cases, scenarios with none, a unique interior fixed point are possible as  changes.  Group's success is sigmoidally dependent on the cooperativeness of the group. Intriguingly, for this pattern, the population dynamics exhibit very rich dynamics: scenarios with none, one and two interior fixed point are possible as  changes. Parameters  and , , and .
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pone-0063801-g001: Population dynamics whenever only cooperators and defectors compete to survive.The intersection of with horizontal line (dashed line) represents the values of fraction of cooperators (if exists) at which payoff of cooperators is equivalent to that of defectors, i.e., . Group's success is inverse-sigmoidally dependent on the cooperativeness of the group. Group's success is linearly dependent on the cooperativeness of the group. In these two cases, scenarios with none, a unique interior fixed point are possible as changes. Group's success is sigmoidally dependent on the cooperativeness of the group. Intriguingly, for this pattern, the population dynamics exhibit very rich dynamics: scenarios with none, one and two interior fixed point are possible as changes. Parameters and , , and .

Mentions: Before entering into the full model admitting all the three strategies, we first consider the special cases where the Loner strategy is absent (i.e., ). In the absence of the loners, the replicator equation suffices to character the population dynamics where means the time evolution of the abundance of cooperators. Cooperators and defectors compete to survive. The group size of interacting individuals remains unchanged over time. The payoff difference of cooperators and defectors reads . By setting , we can obtain , equivalent to the dominance of defectors over cooperators. Whenever the success of the production of common resource linearly relies on the cooperativeness of the group, say , we can accurately derive the mathematical formula of as (see Text S1). As for inverse-sigmoidally cooperativeness-dependent and sigmoidal cooperativeness-dependent patterns, there is no possibility to get the simple mathematical expression of . We can nonetheless look into the properties of the algebraic equation by numerical solving. Figure demonstrates that there exists a threshold value of for the three patterns. For , defectors outperform cooperators, driving the population towards the full defective state, irrespective of the initial frequency ratio of the two strategy types. If the reverse of the inequality is true (i.e, ), the population dynamics vary with the risk removal pattern. In both cases where the success depends inverse-sigmoidally and linearly on the group's cooperativeness, the system has a unique interior unstable fixed point (Figure 1A, 1B), suggesting that the evolutionary fate of cooperators crucially depends on the initial abundance of cooperators. The abundance of cooperators evolves to ever lower value if the initial fraction of cooperators is and the population ends up with all defectors, but to ever higher value and cooperation gets stabilized if .


The increased risk of joint venture promotes social cooperation.

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

Population dynamics whenever only cooperators and defectors compete to survive.The intersection of  with horizontal line  (dashed line) represents the values of fraction of cooperators  (if  exists) at which payoff of cooperators is equivalent to that of defectors, i.e., .  Group's success is inverse-sigmoidally dependent on the cooperativeness of the group.  Group's success is linearly dependent on the cooperativeness of the group. In these two cases, scenarios with none, a unique interior fixed point are possible as  changes.  Group's success is sigmoidally dependent on the cooperativeness of the group. Intriguingly, for this pattern, the population dynamics exhibit very rich dynamics: scenarios with none, one and two interior fixed point are possible as  changes. Parameters  and , , and .
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3672156&req=5

pone-0063801-g001: Population dynamics whenever only cooperators and defectors compete to survive.The intersection of with horizontal line (dashed line) represents the values of fraction of cooperators (if exists) at which payoff of cooperators is equivalent to that of defectors, i.e., . Group's success is inverse-sigmoidally dependent on the cooperativeness of the group. Group's success is linearly dependent on the cooperativeness of the group. In these two cases, scenarios with none, a unique interior fixed point are possible as changes. Group's success is sigmoidally dependent on the cooperativeness of the group. Intriguingly, for this pattern, the population dynamics exhibit very rich dynamics: scenarios with none, one and two interior fixed point are possible as changes. Parameters and , , and .
Mentions: Before entering into the full model admitting all the three strategies, we first consider the special cases where the Loner strategy is absent (i.e., ). In the absence of the loners, the replicator equation suffices to character the population dynamics where means the time evolution of the abundance of cooperators. Cooperators and defectors compete to survive. The group size of interacting individuals remains unchanged over time. The payoff difference of cooperators and defectors reads . By setting , we can obtain , equivalent to the dominance of defectors over cooperators. Whenever the success of the production of common resource linearly relies on the cooperativeness of the group, say , we can accurately derive the mathematical formula of as (see Text S1). As for inverse-sigmoidally cooperativeness-dependent and sigmoidal cooperativeness-dependent patterns, there is no possibility to get the simple mathematical expression of . We can nonetheless look into the properties of the algebraic equation by numerical solving. Figure demonstrates that there exists a threshold value of for the three patterns. For , defectors outperform cooperators, driving the population towards the full defective state, irrespective of the initial frequency ratio of the two strategy types. If the reverse of the inequality is true (i.e, ), the population dynamics vary with the risk removal pattern. In both cases where the success depends inverse-sigmoidally and linearly on the group's cooperativeness, the system has a unique interior unstable fixed point (Figure 1A, 1B), suggesting that the evolutionary fate of cooperators crucially depends on the initial abundance of cooperators. The abundance of cooperators evolves to ever lower value if the initial fraction of cooperators is and the population ends up with all defectors, but to ever higher value and cooperation gets stabilized if .

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