Boltzmann-Based Distributed Replicator Dynamics: A Smart Grid Application

Multi-agent systems (MAS) have been recently used to overcome problems in the control field. The development of distributed control techniques has proven to be an effective approach capable of addressing issues such as communication constraints between agents, modeling of scenarios closer to reality, use of high computational requirements, and understanding of the system complexity. Game theory supports the understanding of interactions between agents, where strategies play a determinant role to maximize agent outcomes. Evolutionary game theory (EGT) has introduced the concept of biological evolution, which has proven to deal with applications that can be modeled using population dynamics.In this work, we consider the replicator dynamics (RD) and propose the use of the Boltzmann model as a base to introduce the Boltzmann-Based Distributed Replicator Dynamics (BBDRD). This novel approach can deal with engineering applications, where the modeling of the system needs no complete information to find the outcome. This proposal allows obtaining a more realistic scenario and gives another perspective to tackle issues with partial information. To understand the behavior of the BBDRD, its use in a smart grid application is validated.