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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.


Distribution of the investments Ii,j over network’s links for different values of the resource allocation parameter α at the steady state. A radical change in the distribution is observed from the static case α=0 (a), in which the investments follow the degree distribution of the underlying network, to the profit-driven case α>0 (b–d) in which the invested quantity in a game is related to the previously earned pay-off in that game. For dynamic resource allocation and α>1.0 (c,d) a two-peaked distribution appears where players decide to put almost the totality of their resources in one game and invest a minimal quantity in other games. The substrate topology is an uncorrelated scale-free network [55] with exponent γ=2.5 and N=104 nodes. The synergy factor r is set to r=4.0 and c=1.
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RSOS170092F3: Distribution of the investments Ii,j over network’s links for different values of the resource allocation parameter α at the steady state. A radical change in the distribution is observed from the static case α=0 (a), in which the investments follow the degree distribution of the underlying network, to the profit-driven case α>0 (b–d) in which the invested quantity in a game is related to the previously earned pay-off in that game. For dynamic resource allocation and α>1.0 (c,d) a two-peaked distribution appears where players decide to put almost the totality of their resources in one game and invest a minimal quantity in other games. The substrate topology is an uncorrelated scale-free network [55] with exponent γ=2.5 and N=104 nodes. The synergy factor r is set to r=4.0 and c=1.

Mentions: Figure 3 depicts how players distribute their investments over the games for all the players once the system reached a stationary state. Here Ii,j represents the fraction of player i’s capital invested in the game centred on player j while P(Ii,j) stands for its distribution over all the players in the system.Figure 3


Heterogeneous resource allocation can change social hierarchy in public goods games
Distribution of the investments Ii,j over network’s links for different values of the resource allocation parameter α at the steady state. A radical change in the distribution is observed from the static case α=0 (a), in which the investments follow the degree distribution of the underlying network, to the profit-driven case α>0 (b–d) in which the invested quantity in a game is related to the previously earned pay-off in that game. For dynamic resource allocation and α>1.0 (c,d) a two-peaked distribution appears where players decide to put almost the totality of their resources in one game and invest a minimal quantity in other games. The substrate topology is an uncorrelated scale-free network [55] with exponent γ=2.5 and N=104 nodes. The synergy factor r is set to r=4.0 and c=1.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

RSOS170092F3: Distribution of the investments Ii,j over network’s links for different values of the resource allocation parameter α at the steady state. A radical change in the distribution is observed from the static case α=0 (a), in which the investments follow the degree distribution of the underlying network, to the profit-driven case α>0 (b–d) in which the invested quantity in a game is related to the previously earned pay-off in that game. For dynamic resource allocation and α>1.0 (c,d) a two-peaked distribution appears where players decide to put almost the totality of their resources in one game and invest a minimal quantity in other games. The substrate topology is an uncorrelated scale-free network [55] with exponent γ=2.5 and N=104 nodes. The synergy factor r is set to r=4.0 and c=1.
Mentions: Figure 3 depicts how players distribute their investments over the games for all the players once the system reached a stationary state. Here Ii,j represents the fraction of player i’s capital invested in the game centred on player j while P(Ii,j) stands for its distribution over all the players in the system.Figure 3

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.