Adaptive and bounded investment returns promote cooperation in spatial public goods games

TL;DR

This paper demonstrates that adaptive and bounded investment returns, which vary based on local and global environments, significantly promote cooperation in spatial public goods games, especially with appropriate feedback strength and limits.

Contribution

It introduces a model where the multiplication factor adapts based on local and global conditions within bounds, enhancing cooperation compared to fixed, uniform factors.

Findings

Full cooperation achieved with high feedback strength and proper limits.

Larger bounds on the multiplication factor increase overall cooperation.

Adaptive bounds outperform fixed multiplication factors in promoting cooperation.

Abstract

The public goods game is one of the most famous models for studying the evolution of cooperation in sizable groups. The multiplication factor in this game can characterize the investment return from the public good, which may be variable depending on the interactive environment in realistic situations. Instead of using the same universal value, here we consider that the multiplication factor in each group is updated based on the differences between the local and global interactive environments in the spatial public goods game, but meanwhile limited to within a certain range. We find that the adaptive and bounded investment returns can significantly promote cooperation. In particular, full cooperation can be achieved for high feedback strength when appropriate limitation is set for the investment return. Also, we show that the fraction of cooperators in the whole population can become larger if the lower and upper limits of the multiplication factor are increased. Furthermore, in comparison to the traditionally spatial public goods game where the multiplication factor in each group is identical and fixed, we find that cooperation can be better promoted if the multiplication factor is constrained to adjust between one and the group size in our model. Our results highlight the importance of the locally adaptive and bounded investment returns for the emergence and dominance of cooperative behavior in structured populations.