# Evolutionary dynamics of group cooperation with asymmetrical environmental feedback

## TL;DR

This paper investigates how asymmetrical environmental feedback influences the evolution of cooperation in multi-player public goods games, revealing conditions for sustained cooperation through oscillatory dynamics.

## Contribution

It extends evolutionary game theory to multi-player settings with asymmetrical feedback, highlighting the role of feedback speed in maintaining cooperation.

## Key findings

- Asymmetrical feedback can lead to oscillatory convergence to cooperation.
- Fast enough changes in cooperation environment promote persistent cooperation.
- The model applies to microbial cooperation and crowdsourcing scenarios.

## Abstract

In recent years, there has been growing interest in studying evolutionary games with environmental feedback. Previous studies exclusively focus on two-player games. However, extension to multi-player game is needed to study problems such as microbial cooperation and crowdsourcing collaborations. Here, we study coevolutionary public goods games where strategies coevolve with the multiplication factors of group cooperation. Asymmetry can arise in such environmental feedback, where games organized by focal cooperators may have a different efficiency than the ones by defectors. Our analysis shows that co-evolutionary dynamics with asymmetrical environmental feedback can yield oscillatory convergence to persistent cooperation, if the relative changing speed of cooperators' multiplication factor is above a certain threshold. Our work provides useful insights into sustaining group cooperation in a changing world.