An evolutionary game perspective on quantised consensus in opinion dynamics

Quantised consensus has been used in the context of opinion dynamics. In this context agents interact with their neighbours and they change their opinion according to their interests and the opinions of their neighbours. We consider various quantised consensus models, where agents have different levels of susceptibility to the inputs received from their neighbours. The provided models share similarities with collective decision making models inspired by honeybees and evolutionary games. As first contribution, we develop an evolutionary game-theoretic model that accommodates the different consensus dynamics in a unified framework. As second contribution, we study equilibrium points and extend such study to the symmetric case where the transition probabilities of the evolutionary game dynamics are symmetric. Symmetry is associated with the case of equally favourable options. As third contribution, we study stability of the equilibrium points for the different cases. We corroborate the theoretical results with some simulations to study the outcomes of the various models.