Modelling the coevolution of opinion dynamics and decision making in social dilemmas
This work addresses the challenge of understanding social behavior dynamics for researchers in game theory and opinion dynamics, but it is incremental as it builds on existing models like the Friedkin-Johnsen model.
The paper tackles the problem of modeling how opinions and actions coevolve in social dilemmas, specifically in a Public Goods Game, by proposing a coevolutionary game that combines payoff from the game with opinion dynamics. The result includes conditions for the existence of all-defection and all-cooperation equilibria and global convergence to all-defection.
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.