Replicator based on imitation for finite and arbitrary networked communities

Abstract

This paper introduces a novel replicator equations to cover evolutionary games. This replicator is applied on a finite set of agent communities organized on arbitrary graphs. The communities located at the nodes of the graph compete with their neighbours according to the weights of the links that connect them. The communities replicate by imitation probabilities those neighbourhood’s strategies with higher utility. The communities also execute a best response addressed to maximize the entropy associated to imitation probabilities. We explore possible connexions between our replicator equations and The Second Law of Thermodynamics, and prove that populations reach consensus equilibria as expressions of maximum entropy states. We also explore connexions with learning dynamics, and prove that under suitable assumptions and conditions, the communities carry out and intelligent learning process. We illustrate results with an example of the classical hawk-dove game applied on fully-connected and arbitrary populations.