# Determinants of public cooperation in multiplex networks

## TL;DR

This paper investigates how the structure and overlap of layers in multiplex networks influence the emergence of public cooperation, revealing that significant link overlap and high synergy factors are crucial for cooperation to thrive.

## Contribution

It uncovers the combined effects of layer overlap and synergy parameters on cooperation in multiplex networks, a novel insight into layered social system dynamics.

## Key findings

- High cooperation requires significant link overlap and high synergy factors.
- Without overlap or high synergy, cooperation follows traditional network reciprocity.
- Results challenge optimistic views on multiplex networks inherently promoting cooperation.

## Abstract

Synergies between evolutionary game theory and statistical physics have significantly improved our understanding of public cooperation in structured populations. Multiplex networks, in particular, provide the theoretical framework within network science that allows us to mathematically describe the rich structure of interactions characterizing human societies. While research has shown that multiplex networks may enhance the resilience of cooperation, the interplay between the overlap in the structure of the layers and the control parameters of the corresponding games has not yet been investigated. With this aim, we consider here the public goods game on a multiplex network, and we unveil the role of the number of layers and the overlap of links, as well as the impact of different synergy factors in different layers, on the onset of cooperation. We show that enhanced public cooperation emerges only when a significant edge overlap is combined with at least one layer being able to sustain some cooperation by means of a sufficiently high synergy factor. In the absence of either of these conditions, the evolution of cooperation in multiplex networks is determined by the bounds of traditional network reciprocity with no enhanced resilience. These results caution against overly optimistic predictions that the presence of multiple social domains may in itself promote cooperation, and they help us better understand the complexity behind prosocial behavior in layered social systems.