Game Theory and Multi-Agent Reinforcement Learning: A Mathematical Overview

Abstract

This paper provides a comprehensive examination of the mathematical foundations and applications of Game Theory and Multi-Agent Reinforcement Learning (MARL), focusing on their intersections and practical implications. Game Theory, rooted in mathematics and economics, offers a structured approach to analyzing strategic interactions among rational decision-makers, introducing essential concepts such as Nash equilibrium and subgame perfect equilibrium. These concepts are critical for modeling scenarios in economics, political science, and artificial intelligence, where the decisions of one player significantly impact the outcomes of others. The paper also explores MARL, which extends reinforcement learning to multi-agent environments, addressing challenges like non-stationarity and the need for scalable algorithms. By covering algorithms such as Independent Q-Learning, Deep Q-Networks, and Policy Gradient methods, the paper highlights MARL's applications in areas like robotics, traffic management, and financial markets. Additionally, the integration of Game Theory with MARL is discussed, emphasizing how game-theoretic concepts enhance the development of MARL algorithms, particularly in optimizing trading strategies and market behavior in financial contexts.

Keywords: reinforcement learning, gametheory, artificial intelligence

JEL Classification: C63, C72, C71, C78, C81, C83, C61, C65, C17, C14