# Promoting cooperation by preventing exploitation: The role of network structure

## TL;DR

This paper investigates how network structure influences cooperation through a generalized reciprocity mechanism, highlighting the role of neighborhood importance and analyzing robustness against defectors in social and artificial systems.

## Contribution

It introduces a network-based model of generalized reciprocity, linking cooperation levels to a new centrality measure, and examines its robustness against defectors.

## Key findings

- Cooperation propensity depends on neighborhood importance index.
- Network structure significantly affects cooperation dynamics.
- The model remains robust even with some unconditional defectors.

## Abstract

A growing body of empirical evidence indicates that social and cooperative behavior can be affected by cognitive and neurological factors, suggesting the existence of state-based decision-making mechanisms that may have emerged by evolution. Motivated by these observations, we propose a simple mechanism of anonymous network interactions identified as a form of generalized reciprocity - a concept organized around the premise "help anyone if helped by someone", and study its dynamics on random graphs. In the presence of such mechanism, the evolution of cooperation is related to the dynamics of the levels of investments (i.e. probabilities of cooperation) of the individual nodes engaging in interactions. We demonstrate that the propensity for cooperation is determined by a network centrality measure here referred to as neighborhood importance index and discuss relevant implications to natural and artificial systems. To address the robustness of the state-based strategies to an invasion of defectors, we additionally provide an analysis which redefines the results for the case when a fraction of the nodes behave as unconditional defectors.