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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.

No MeSH data available.


Visualization of the networks obtained considering only negative (a) and positive (b) links from the same original network of size N=300. The original graph is a scale-free network generated according to the uncorrelated configuration model [55] with γ=2.5 and N=300 nodes.
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RSOS170092F6: Visualization of the networks obtained considering only negative (a) and positive (b) links from the same original network of size N=300. The original graph is a scale-free network generated according to the uncorrelated configuration model [55] with γ=2.5 and N=300 nodes.

Mentions: By analysing how the two types of links are organized, we can dissect the entire network in two subgraphs: one formed only by negative links and the other containing the positive ones. The analysis of the two networks brings about interesting results. We found that in almost all the realizations the two networks were connected graphs (only in a few cases the positive network presented some isolated nodes) and, more importantly, in all the cases, the positive network had a backbone-like structure with similar topological features of the minimum spanning tree of the original network. On the other hand, the negative network always includes the majority of the links and its structure strictly resembles the original one (the details of the topological analysis and the comparison between the positive network and the minimum spanning tree are given in the electronic supplementary material). Also visually (figure 6) the differences between the two networks is notable, with the positive network formed by long chains of poorly connected nodes resembling the spanning tree. It is worth stressing that this backbone organization of the links at the entire network level spontaneously emerges as a consequence of the self-organization of the players at the local level without any control mechanism.Figure 6


Heterogeneous resource allocation can change social hierarchy in public goods games
Visualization of the networks obtained considering only negative (a) and positive (b) links from the same original network of size N=300. The original graph is a scale-free network generated according to the uncorrelated configuration model [55] with γ=2.5 and N=300 nodes.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

RSOS170092F6: Visualization of the networks obtained considering only negative (a) and positive (b) links from the same original network of size N=300. The original graph is a scale-free network generated according to the uncorrelated configuration model [55] with γ=2.5 and N=300 nodes.
Mentions: By analysing how the two types of links are organized, we can dissect the entire network in two subgraphs: one formed only by negative links and the other containing the positive ones. The analysis of the two networks brings about interesting results. We found that in almost all the realizations the two networks were connected graphs (only in a few cases the positive network presented some isolated nodes) and, more importantly, in all the cases, the positive network had a backbone-like structure with similar topological features of the minimum spanning tree of the original network. On the other hand, the negative network always includes the majority of the links and its structure strictly resembles the original one (the details of the topological analysis and the comparison between the positive network and the minimum spanning tree are given in the electronic supplementary material). Also visually (figure 6) the differences between the two networks is notable, with the positive network formed by long chains of poorly connected nodes resembling the spanning tree. It is worth stressing that this backbone organization of the links at the entire network level spontaneously emerges as a consequence of the self-organization of the players at the local level without any control mechanism.Figure 6

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.