# Cooperation dynamics in the networked geometric Brownian motion

## TL;DR

This paper explores how network structures influence cooperation among individuals sharing resources in fluctuating environments modeled by geometric Brownian motion, revealing complex effects on resource distribution and growth.

## Contribution

It introduces a model for networked pooling and sharing in fluctuating environments, highlighting the impact of topology on cooperation dynamics and resource distribution.

## Key findings

- Cooperation generally enhances individual growth rates.
- Network topology causes significant disparities in resource endowments.
- The interplay between cooperation and network structure affects evolutionary outcomes.

## Abstract

Recent works suggest that pooling and sharing may constitute a fundamental mechanism for the evolution of cooperation in well-mixed fluctuating environments. The rationale is that, by reducing the amplitude of fluctuations, pooling and sharing increases the steady-state growth rate at which the individuals self-reproduce. However, in reality interactions are seldom realized in a well-mixed structure, and the underlying topology is in general described by a complex network. Motivated by this observation, we investigate the role of the network structure on the cooperative dynamics in fluctuating environments, by developing a model for networked pooling and sharing of resources undergoing environmental fluctuations, represented through geometric Brownian motion. The study reveals that, while in general cooperation increases the individual steady state growth rates (i.e. is evolutionary advantageous), the interplay with the network structure may yield large discrepancies in the observed individual resource endowments. We comment possible biological and social implications and discuss relations to econophysics.