Learning in Networked Interactions: A Replicator Dynamics Approach

Many real-world scenarios can be modelled as multi-agent systems, where multiple autonomous decision makers interact in a single environment. The complex and dynamic nature of such interactions prevents hand-crafting solutions for all possible scenarios, hence learning is crucial. Studying the dynamics of multi-agent learning is imperative in selecting and tuning the right learning algorithm for the task at hand. So far, analysis of these dynamics has been mainly limited to normal form games, or unstructured populations. However, many multi-agent systems are highly structured, complex networks, with agents only interacting locally. Here, we study the dynamics of such networked interactions, using the well-known replicator dynamics of evolutionary game theory as a model for learning. Different learning algorithms are modelled by altering the replicator equations slightly. In particular, we investigate lenience as an enabler for cooperation. Moreover, we show how well-connected, stubborn agents can influence the learning outcome. Finally, we investigate the impact of structural network properties on the learning outcome, as well as the influence of mutation driven by exploration.