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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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Triangle plots illustrating the population dynamics for defectors (), cooperators () and loners () for trajectories starting from all possible initial frequencies for the linear risk removal pattern.Each vertex represents a homogeneous population of that pure strategy.  For small interest rate , there is only one nontrivial fixed point () located inside the simplex . All trajectories starting from inside of the simplex  invariable lead to the unique convergent equilibrium .  For modest , except , there also exists another nontrivial fixed point located in the line  (). Instead the cooperators' attraction basin covers absolutely large fraction of the inside area of the simplex , and loners' attraction basin is almost negligible. If defectors are abundant, the population dynamics oscillate around the unique unstable interior fixed point  with increasing amplitude and eventually converges to the full cooperative state . Otherwise, the population directly drives towards .  Further increase in  continue to expand the cooperators' attraction basin. It should be noted that even , loners' attraction basin, albeit narrows, does not vanish. Relevant parameters ,  and , , .
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pone-0063801-g006: Triangle plots illustrating the population dynamics for defectors (), cooperators () and loners () for trajectories starting from all possible initial frequencies for the linear risk removal pattern.Each vertex represents a homogeneous population of that pure strategy. For small interest rate , there is only one nontrivial fixed point () located inside the simplex . All trajectories starting from inside of the simplex invariable lead to the unique convergent equilibrium . For modest , except , there also exists another nontrivial fixed point located in the line (). Instead the cooperators' attraction basin covers absolutely large fraction of the inside area of the simplex , and loners' attraction basin is almost negligible. If defectors are abundant, the population dynamics oscillate around the unique unstable interior fixed point with increasing amplitude and eventually converges to the full cooperative state . Otherwise, the population directly drives towards . Further increase in continue to expand the cooperators' attraction basin. It should be noted that even , loners' attraction basin, albeit narrows, does not vanish. Relevant parameters , and , , .

Mentions: We now full characterize the population dynamics by a three dimensional simplex , whose each point has three components denoting the fractions of cooperators, defectors, and loners respectively. For , a small enhancement factor divides the inside of the simplex into two attraction areas, with the larger one being the loners' and the other one cooperators' (Figure 5A). In both linearly and sigmoidally cooperativeness-dependent patterns, the same enhancement factor leads to that loners progressively pervade the entire population and eventually dominate, reflecting by that each orbit starting from any point inside , with exception of fixed points if they do exist, drives towards and ends at the pure state of loners (Figure 6A, 7A), resembling the results widely reported in the public enterprizes absent of risk. This distinction can be attributed to the following interpretations. As have established, loner is the payoff-maximizing strategy for small in the absence of the failure risk. The presence of risk indeed reduces the expected payoff of both defectors and cooperators in comparison to most traditional studies (i.e., without risk) for identical group composition. Payoff of loners remains unaffected. Though depending on the cooperativeness, the group's success is not so hard in the linear and sigmoidal patterns as that in the inverse-sigmoidal pattern, therefore defectors parasited in groups of most cooperators and loners have much more chances to hitch cooperators' contribution. The exploitation induces the evolutionary trajectory to move forward along the direction of increasing defectors, who are emulated by the loners. Differently, as the group's success is such strongly on its cooperativeness for , the successful group must bring much payoff for cooperators than for defectors, thus the trajectory starting in the area covering immensely few defectors would drive towards the full cooperative state.


The increased risk of joint venture promotes social cooperation.

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

Triangle plots illustrating the population dynamics for defectors (), cooperators () and loners () for trajectories starting from all possible initial frequencies for the linear risk removal pattern.Each vertex represents a homogeneous population of that pure strategy.  For small interest rate , there is only one nontrivial fixed point () located inside the simplex . All trajectories starting from inside of the simplex  invariable lead to the unique convergent equilibrium .  For modest , except , there also exists another nontrivial fixed point located in the line  (). Instead the cooperators' attraction basin covers absolutely large fraction of the inside area of the simplex , and loners' attraction basin is almost negligible. If defectors are abundant, the population dynamics oscillate around the unique unstable interior fixed point  with increasing amplitude and eventually converges to the full cooperative state . Otherwise, the population directly drives towards .  Further increase in  continue to expand the cooperators' attraction basin. It should be noted that even , loners' attraction basin, albeit narrows, does not vanish. Relevant parameters ,  and , , .
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3672156&req=5

pone-0063801-g006: Triangle plots illustrating the population dynamics for defectors (), cooperators () and loners () for trajectories starting from all possible initial frequencies for the linear risk removal pattern.Each vertex represents a homogeneous population of that pure strategy. For small interest rate , there is only one nontrivial fixed point () located inside the simplex . All trajectories starting from inside of the simplex invariable lead to the unique convergent equilibrium . For modest , except , there also exists another nontrivial fixed point located in the line (). Instead the cooperators' attraction basin covers absolutely large fraction of the inside area of the simplex , and loners' attraction basin is almost negligible. If defectors are abundant, the population dynamics oscillate around the unique unstable interior fixed point with increasing amplitude and eventually converges to the full cooperative state . Otherwise, the population directly drives towards . Further increase in continue to expand the cooperators' attraction basin. It should be noted that even , loners' attraction basin, albeit narrows, does not vanish. Relevant parameters , and , , .
Mentions: We now full characterize the population dynamics by a three dimensional simplex , whose each point has three components denoting the fractions of cooperators, defectors, and loners respectively. For , a small enhancement factor divides the inside of the simplex into two attraction areas, with the larger one being the loners' and the other one cooperators' (Figure 5A). In both linearly and sigmoidally cooperativeness-dependent patterns, the same enhancement factor leads to that loners progressively pervade the entire population and eventually dominate, reflecting by that each orbit starting from any point inside , with exception of fixed points if they do exist, drives towards and ends at the pure state of loners (Figure 6A, 7A), resembling the results widely reported in the public enterprizes absent of risk. This distinction can be attributed to the following interpretations. As have established, loner is the payoff-maximizing strategy for small in the absence of the failure risk. The presence of risk indeed reduces the expected payoff of both defectors and cooperators in comparison to most traditional studies (i.e., without risk) for identical group composition. Payoff of loners remains unaffected. Though depending on the cooperativeness, the group's success is not so hard in the linear and sigmoidal patterns as that in the inverse-sigmoidal pattern, therefore defectors parasited in groups of most cooperators and loners have much more chances to hitch cooperators' contribution. The exploitation induces the evolutionary trajectory to move forward along the direction of increasing defectors, who are emulated by the loners. Differently, as the group's success is such strongly on its cooperativeness for , the successful group must bring much payoff for cooperators than for defectors, thus the trajectory starting in the area covering immensely few defectors would drive towards the full cooperative state.

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