Replicator dynamics with diffusion on multiplex networks

TL;DR

This paper extends replicator dynamics with diffusion to multiplex networks, deriving exact formulas and revealing hidden selective pressures caused by constant population assumptions.

Contribution

It introduces a novel extension of the replicator equation with diffusion on multiplex graphs, including exact formulas and transition probabilities.

Findings

Diffusion is linear for agent numbers but nonlinear for fractions.

Constant population assumptions induce hidden selective pressures.

Derived transition probabilities explain macroscopic behavior.

Abstract

In this study we present an extension of the replicator equation with diffusion to multiplex graphs. We derive an exact formula for the diffusion term, which shows that, while diffusion is linear for numbers of agents, it is necessary to account for non-linear terms when working with fractions of individuals. We also derive the transition probabilities that give rise to such macroscopic behavior, completing the bottom-up description. Finally, it shown that the usual assumption of constant population sizes induces a hidden selective pressure in the system.