Strategy Diffusion and Conformity in Evolutionary Dynamics on General Networks

Networks of social interactions can drive the dynamics of socio-technical systems. In groups, where strategic decisions are shaped by the tension between cooperation and defection, the replicator equation serves as a valuable tool underpinning the modelling of evolutionary dynamics of strategies. In this letter, we integrate the replicator dynamics with an SI (Susceptible-Infected) model for information diffusion in general networks. Considering also conformity, we model the evolution of cooperation in a public good game. The trajectories of the resulting dynamical systems converge to consensus about an internal point solution in the snowdrift setting and boundary solutions of full cooperation or full defection in social dilemmas, asymmetric games and stag hunt settings. Through the application of the Lyapunov stability theorem, we establish the stability of the internal equilibrium point. We then examine the basin of attraction obtaining the conditions leading to full cooperation. This letter is relevant for the study of social dynamics in groups where strategic interactions are mediated by conformity.

I. Introduction

In social and biological systems, it is not uncommon to witness the renounce to selfish benefits for the common good [1]. In general, defecting and selfishly prioritising own reward is the normal course of action. Altruistic behaviours often imply costly choices.