Evolutionary dynamics on a regular networked structured and unstructured multi-population

In this paper, we study collective decision-making in a multi-population framework, where groups of individuals represent whole populations that interact by means of a regular network. Each group consists of a number of players and every player can choose between two options. A group is characterized by three variables, the first two denoting the fractions of individuals committed to each option and the last one representing the fraction of players not committed to either option. The state of every population is influenced by the state of neighboring groups. The contribution of this work is the following. First, we find explicit expressions for all the equilibrium points of the proposed system, and show that these represent equilibrium points where populations reach consensus, namely, where all populations have the same states. We also derive a sufficient condition for local asymptotic stability as well as exponential asymptotic stability. Then, we study a structured model where every population is now assumed to represent a structured complex network. We conclude the paper by providing a set of simulations that corroborate the theoretical findings.