Spillover modes in multiplex games: double-edged effects on cooperation, and their coevolution

TL;DR

This study investigates how different spillover modes across social contexts in multiplex networks influence cooperation, revealing that spillover can both promote and hinder cooperation depending on intensity and initial conditions.

Contribution

It introduces a model analyzing three spillover modes in multiplex networks and compares their effects on cooperation, providing new insights into cross-context behavioral influence.

Findings

Moderate spillover promotes cooperation when it is initially favored.

Excessive spillover can be detrimental to cooperation.

Spillover effects depend on initial cooperation levels and can cause bistability.

Abstract

In recent years, there has been growing interest in studying games on multiplex networks that account for interactions across linked social contexts. However, little is known about how potential cross-context interference, or spillover, of individual behavioural strategy impact overall cooperation. We consider three plausible spillover modes, quantifying and comparing their effects on the evolution of cooperation. In our model, social interactions take place on two network layers: one represents repeated interactions with close neighbours in a lattice, the other represents one-shot interactions with random individuals across the same population. Spillover can occur during the social learning process with accidental cross-layer strategy transfer, or during social interactions with errors in implementation due to contextual interference. Our analytical results, using extended pair approximation, are in good agreement with extensive simulations. We find double-edged effects of spillover on cooperation: increasing the intensity of spillover can promote cooperation provided cooperation is favoured in one layer, but too much spillover is detrimental. We also discover a bistability phenomenon of cooperation: spillover hinders or promotes cooperation depending on initial frequencies of cooperation in each layer. Furthermore, comparing strategy combinations that emerge in each spillover mode provides a good indication of their co-evolutionary dynamics with cooperation. Our results make testable predictions that inspire future research, and sheds light on human cooperation across social domains and their interference with one another.