On the Relation Between Replicator Evolutionary Dynamics and Diffusive Models on General Networks

Understanding how cooperation spreads across social groups is fundamental in predicting how people will interact with each other in relation to the use and exploitation of the resources they are provided with. When social interactions can be mapped to a network, questions arise about the impact of the connection structure which can benefit from the literature developed for a dynamical systems. One model that is widely used as a model to understand the dynamics of cooperation is the replicator equation. While research has been proposed to adapt that equation to a structured graph, we offer a straightforward approach by benefiting from the networked SI diffusion model and replicator equation to create a replicator equation on a network with state-dependent diffusive constant. This approach can be applied to any network structure and features separation of the game and the information diffusion mechanism. The equilibria towards which the system evolves are here characterised and discussed.