  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.
