Boltzmann Distributed Replicator Dynamics: Population Games in a Microgrid Context

Gustavo Chica-Pedraza, Eduardo Mojica-Nava and Ernesto Cadena-Muñoz
Additional contact information
Gustavo Chica-Pedraza: School of Telecommunications Engineering, Universidad Santo Tomás, 110311 Bogotá D.C., Colombia
Eduardo Mojica-Nava: Department of Electric and Electronic Engineering, Universidad Nacional de Colombia, 111321 Bogotá D.C., Colombia
Ernesto Cadena-Muñoz: Department of Systems and Industrial Engineering, Universidad Nacional de Colombia, 111321 Bogotá D.C., Colombia

Games, 2021, vol. 12, issue 1, 1-18

Abstract: Multi-Agent Systems (MAS) have been used to solve several optimization problems in control systems. MAS allow understanding the interactions between agents and the complexity of the system, thus generating functional models that are closer to reality. However, these approaches assume that information between agents is always available, which means the employment of a full-information model. Some tendencies have been growing in importance to tackle scenarios where information constraints are relevant issues. In this sense, game theory approaches appear as a useful technique that use a strategy concept to analyze the interactions of the agents and achieve the maximization of agent outcomes. In this paper, we propose a distributed control method of learning that allows analyzing the effect of the exploration concept in MAS. The dynamics obtained use Q-learning from reinforcement learning as a way to include the concept of exploration into the classic exploration-less Replicator Dynamics equation. Then, the Boltzmann distribution is used to introduce the Boltzmann-Based Distributed Replicator Dynamics as a tool for controlling agents behaviors. This distributed approach can be used in several engineering applications, where communications constraints between agents are considered. The behavior of the proposed method is analyzed using a smart grid application for validation purposes. Results show that despite the lack of full information of the system, by controlling some parameters of the method, it has similar behavior to the traditional centralized approaches.

Keywords: Boltzmann distribution; economic dispatch problem; Multi-Agent Systems; population dynamics; revision protocol (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://www.mdpi.com/2073-4336/12/1/8/pdf (application/pdf)
https://www.mdpi.com/2073-4336/12/1/8/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jgames:v:12:y:2021:i:1:p:8-:d:480801

Access Statistics for this article

Games is currently edited by Ms. Susie Huang

More articles in Games from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().