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Heterogeneous resource allocation can change social hierarchy in public goods games

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ABSTRACT

Public goods games (PGGs) represent one of the most useful tools to study group interactions. However, even if they could provide an explanation for the emergence and stability of cooperation in modern societies, they are not able to reproduce some key features observed in social and economical interactions. The typical shape of wealth distribution—known as Pareto Law—and the microscopic organization of wealth production are two of them. Here, we introduce a modification to the classical formulation of PGGs that allows for the emergence of both of these features from first principles. Unlike traditional PGGs, where players contribute equally to all the games in which they participate, we allow individuals to redistribute their contribution according to what they earned in previous rounds. Results from numerical simulations show that not only a Pareto distribution for the pay-offs naturally emerges but also that if players do not invest enough in one round they can act as defectors even if they are formally cooperators. Our results not only give an explanation for wealth heterogeneity observed in real data but also point to a conceptual change on cooperation in collective dilemmas.

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Cumulative fraction of the total normalized pay-off produced in the network as a function of the nodes ranked from the most productive to the less productive ones for several values of α. The coloured regions depict 80% of the total wealth and the blue circle represents the optimal value where 80% of the wealth is produced by 20% of the nodes. For the static (α=0.0) resource allocation (a), more than 60% of the games is needed to produce 80% of the total wealth while for dynamic resource allocation (α>2.0) almost 20% of the nodes alone produces 80% of the wealth, resembling a Pareto Law [56]. Results represent the average over at least 500 different initial conditions. The other parameters are the same as in figure 3.
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RSOS170092F5: Cumulative fraction of the total normalized pay-off produced in the network as a function of the nodes ranked from the most productive to the less productive ones for several values of α. The coloured regions depict 80% of the total wealth and the blue circle represents the optimal value where 80% of the wealth is produced by 20% of the nodes. For the static (α=0.0) resource allocation (a), more than 60% of the games is needed to produce 80% of the total wealth while for dynamic resource allocation (α>2.0) almost 20% of the nodes alone produces 80% of the wealth, resembling a Pareto Law [56]. Results represent the average over at least 500 different initial conditions. The other parameters are the same as in figure 3.

Mentions: The coloured area in figure 5 indicates 80% of the cumulative fraction of the total normalized pay-off produced by nodes ranked from the most to the least productive ones. In the classical PGG, almost 70% of the nodes are required to reach 80% of the wealth while for α>1.0 this value reaches approximatively 24% and for higher values of α becomes more stable and asymptotically approaches 20% (see the electronic supplementary material). Given that we have not imposed any rule on the PGG other than a stochastic investment mechanism and a replicator-like evolution of the strategies, it can be said that the resulting Pareto Law is obtained from first principles.Figure 5


Heterogeneous resource allocation can change social hierarchy in public goods games
Cumulative fraction of the total normalized pay-off produced in the network as a function of the nodes ranked from the most productive to the less productive ones for several values of α. The coloured regions depict 80% of the total wealth and the blue circle represents the optimal value where 80% of the wealth is produced by 20% of the nodes. For the static (α=0.0) resource allocation (a), more than 60% of the games is needed to produce 80% of the total wealth while for dynamic resource allocation (α>2.0) almost 20% of the nodes alone produces 80% of the wealth, resembling a Pareto Law [56]. Results represent the average over at least 500 different initial conditions. The other parameters are the same as in figure 3.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5383863&req=5

RSOS170092F5: Cumulative fraction of the total normalized pay-off produced in the network as a function of the nodes ranked from the most productive to the less productive ones for several values of α. The coloured regions depict 80% of the total wealth and the blue circle represents the optimal value where 80% of the wealth is produced by 20% of the nodes. For the static (α=0.0) resource allocation (a), more than 60% of the games is needed to produce 80% of the total wealth while for dynamic resource allocation (α>2.0) almost 20% of the nodes alone produces 80% of the wealth, resembling a Pareto Law [56]. Results represent the average over at least 500 different initial conditions. The other parameters are the same as in figure 3.
Mentions: The coloured area in figure 5 indicates 80% of the cumulative fraction of the total normalized pay-off produced by nodes ranked from the most to the least productive ones. In the classical PGG, almost 70% of the nodes are required to reach 80% of the wealth while for α>1.0 this value reaches approximatively 24% and for higher values of α becomes more stable and asymptotically approaches 20% (see the electronic supplementary material). Given that we have not imposed any rule on the PGG other than a stochastic investment mechanism and a replicator-like evolution of the strategies, it can be said that the resulting Pareto Law is obtained from first principles.Figure 5

View Article: PubMed Central - PubMed

ABSTRACT

Public goods games (PGGs) represent one of the most useful tools to study group interactions. However, even if they could provide an explanation for the emergence and stability of cooperation in modern societies, they are not able to reproduce some key features observed in social and economical interactions. The typical shape of wealth distribution—known as Pareto Law—and the microscopic organization of wealth production are two of them. Here, we introduce a modification to the classical formulation of PGGs that allows for the emergence of both of these features from first principles. Unlike traditional PGGs, where players contribute equally to all the games in which they participate, we allow individuals to redistribute their contribution according to what they earned in previous rounds. Results from numerical simulations show that not only a Pareto distribution for the pay-offs naturally emerges but also that if players do not invest enough in one round they can act as defectors even if they are formally cooperators. Our results not only give an explanation for wealth heterogeneity observed in real data but also point to a conceptual change on cooperation in collective dilemmas.

No MeSH data available.


Related in: MedlinePlus