Reinforcement learning (RL) is a type of machine learning where an agent learns optimal behavior through interaction with its environment. It is a machine learning training method that trains software to make certain desired actions. Nash equilibrium (SNE) is a combination of actions of the different players, in which no coalition of players can cooperatively deviate. Each player chooses the best strategy among all options. Nash equilibrium occurs when each player knows the strategy of their opponent and uses that knowledge. Nash equilibrium occurs in non-cooperative games when two players have optimal game strategies such that no matter how they change their strategy. This paper explores the application of reinforcement learning algorithms within the domain of game theory, with a particular focus on their convergence properties toward Nash equilibrium. We analyze q-learning approach in 2-agent environments, highlighting their capacity to learn optimal strategies through iterative interactions. Our theoretical investigation examines the conditions under which these algorithms converge to Nash equilibrium, considering factors such as learning rate schedules. The insights gained contribute to a deeper understanding of how reinforcement learning can serve as a powerful tool for equilibrium computation in complex strategic environments, paving the way for advanced applications in economics, automated negotiations, and autonomous systems.
| Published in | Mathematics Letters (Volume 11, Issue 3) |
| DOI | 10.11648/j.ml.20251103.12 |
| Page(s) | 66-70 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2025. Published by Science Publishing Group |
Q-learning, Nash Equilibrium, Game Theory, Reinforcement Learning
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APA Style
Habibi, R. (2025). Use of Reinforcement Learning to Gain the Nash Equilibrium. Mathematics Letters, 11(3), 66-70. https://doi.org/10.11648/j.ml.20251103.12
ACS Style
Habibi, R. Use of Reinforcement Learning to Gain the Nash Equilibrium. Math. Lett. 2025, 11(3), 66-70. doi: 10.11648/j.ml.20251103.12
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Download@article{10.11648/j.ml.20251103.12,
author = {Reza Habibi},
title = {Use of Reinforcement Learning to Gain the Nash Equilibrium
},
journal = {Mathematics Letters},
volume = {11},
number = {3},
pages = {66-70},
doi = {10.11648/j.ml.20251103.12},
url = {https://doi.org/10.11648/j.ml.20251103.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20251103.12},
abstract = {Reinforcement learning (RL) is a type of machine learning where an agent learns optimal behavior through interaction with its environment. It is a machine learning training method that trains software to make certain desired actions. Nash equilibrium (SNE) is a combination of actions of the different players, in which no coalition of players can cooperatively deviate. Each player chooses the best strategy among all options. Nash equilibrium occurs when each player knows the strategy of their opponent and uses that knowledge. Nash equilibrium occurs in non-cooperative games when two players have optimal game strategies such that no matter how they change their strategy. This paper explores the application of reinforcement learning algorithms within the domain of game theory, with a particular focus on their convergence properties toward Nash equilibrium. We analyze q-learning approach in 2-agent environments, highlighting their capacity to learn optimal strategies through iterative interactions. Our theoretical investigation examines the conditions under which these algorithms converge to Nash equilibrium, considering factors such as learning rate schedules. The insights gained contribute to a deeper understanding of how reinforcement learning can serve as a powerful tool for equilibrium computation in complex strategic environments, paving the way for advanced applications in economics, automated negotiations, and autonomous systems.
},
year = {2025}
}
TY - JOUR T1 - Use of Reinforcement Learning to Gain the Nash Equilibrium AU - Reza Habibi Y1 - 2025/10/31 PY - 2025 N1 - https://doi.org/10.11648/j.ml.20251103.12 DO - 10.11648/j.ml.20251103.12 T2 - Mathematics Letters JF - Mathematics Letters JO - Mathematics Letters SP - 66 EP - 70 PB - Science Publishing Group SN - 2575-5056 UR - https://doi.org/10.11648/j.ml.20251103.12 AB - Reinforcement learning (RL) is a type of machine learning where an agent learns optimal behavior through interaction with its environment. It is a machine learning training method that trains software to make certain desired actions. Nash equilibrium (SNE) is a combination of actions of the different players, in which no coalition of players can cooperatively deviate. Each player chooses the best strategy among all options. Nash equilibrium occurs when each player knows the strategy of their opponent and uses that knowledge. Nash equilibrium occurs in non-cooperative games when two players have optimal game strategies such that no matter how they change their strategy. This paper explores the application of reinforcement learning algorithms within the domain of game theory, with a particular focus on their convergence properties toward Nash equilibrium. We analyze q-learning approach in 2-agent environments, highlighting their capacity to learn optimal strategies through iterative interactions. Our theoretical investigation examines the conditions under which these algorithms converge to Nash equilibrium, considering factors such as learning rate schedules. The insights gained contribute to a deeper understanding of how reinforcement learning can serve as a powerful tool for equilibrium computation in complex strategic environments, paving the way for advanced applications in economics, automated negotiations, and autonomous systems. VL - 11 IS - 3 ER -
Deaprtment of Banking, Iran Banking Institute, Tehran, Iran
