Replicator Dynamics for Multi-agent Learning: An Orthogonal Approach

Today's society is largely connected and many real life applications lend themselves to be modeled as multi-agent systems. Although such systems as well as their models are desirable, e.g., for reasons of stability or parallelism, they are highly complex and therefore difficult to understand or predict. Multi-agent learning has been acknowledged to be indispensable to control or find solutions for such systems. Recently, evolutionary game theory has been linked to multi-agent reinforcement learning. However, gaining insight into the dynamics of games, especially if time dependent, remains a challenging problem. This article introduces a new perspective on the reinforcement learning process described by the replicator dynamics, providing a tool to design time dependent parameters of the game or the learning process. This perspective is orthogonal to the common view of policy trajectories driven by the replicator dynamics. Rather than letting the time dimension collapse, the set of initial policies is considered to be a particle cloud that approximates a distribution and we look at the evolution of this distribution over time. First, the methodology is described, then it is applied to an example game and viable extensions are discussed.