Modelling the coevolution of opinion dynamics and decision making in social dilemmas

TL;DR

This paper introduces a mathematical model combining opinion dynamics and decision-making in social dilemmas, specifically within a Public Goods Game, analyzing equilibria and convergence properties.

Contribution

It presents a novel coevolutionary game model integrating PGG and Friedkin--Johnsen opinion dynamics, with analysis of equilibria and convergence conditions.

Findings

Conditions for all-defection and all-cooperation equilibria are derived.

The model demonstrates global convergence to the all-defection equilibrium under certain conditions.

The coevolutionary dynamics are characterized through a discrete-time asynchronous update process.

Abstract

This paper proposes a mathematical model for the coevolution of actions and opinions for a population facing a social dilemma. In particular, we assume each person participates in a Public Goods Game (PGG), with their action being to cooperate or defect, and holds an opinion about which action they prefer. We propose a payoff function that combines the PGG with the Friedkin--Johnsen model from opinion dynamics to form a coevolutionary game. According to a discrete-time process, players asynchronously update their actions and opinions, aiming to maximise their individual payoff for the coevolutionary game using myopic best-response. We study the equilibria and provide conditions for the existence of the all-defection and all-cooperation consensus equilibria. We also establish conditions for global convergence to the all-defection equilibrium.