Heterogeneous resource allocation can change social hierarchy in public goods games

TL;DR

This paper modifies Public Goods Games to incorporate resource redistribution based on past earnings, leading to the emergence of wealth distributions resembling Pareto Law and revealing new insights into cooperation dynamics.

Contribution

It introduces a novel resource redistribution mechanism in Public Goods Games that reproduces wealth heterogeneity and alters cooperation behavior from first principles.

Findings

Pareto distribution naturally emerges in the model

Players can defect despite being cooperators due to low investment

Players self-organize into a backbone resembling the minimum spanning tree

Abstract

Public Goods Games represent one of the most useful tools to study group interactions between individuals. 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 Public Goods Games that allows for the emergence of both of these features from first principles. Unlike traditional Public Goods Games on networks, 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 payoffs naturally emerges but also that if players don't invest enough in one round they can act as defectors even if they are formally cooperators. Finally, we also show that the players self-organize in a very productive backbone that covers almost perfectly the minimum spanning tree of the underlying interaction network. Our results not only give an explanation for the presence of the wealth heterogeneity observed in real data but also points to a conceptual change regarding how cooperation is defined in collective dilemmas.