Modeling opponent learning in multiagent repeated games

Abstract

Multiagent reinforcement learning (MARL) has been used extensively in the game environment. One of the main challenges in MARL is that the environment of the agent system is dynamic, and the other agents are also updating their strategies. Therefore, modeling the opponents’ learning process and adopting specific strategies to shape learning is an effective way to obtain better training results. Previous studies such as DRON, LOLA and SOS approximated the opponent’s learning process and gave effective applications. However, these studies modeled only transient changes in opponent strategies and lacked stability in the improvement of equilibrium efficiency. In this article, we design the MOL (modeling opponent learning) method based on the Stackelberg game. We use best response theory to approximate the opponents’ preferences for different actions and explore stable equilibrium with higher rewards. We find that MOL achieves better results in several games with classical structures (the Prisoner’s Dilemma, Stackelberg Leader game and Stag Hunt with 3 players), and in randomly generated bimatrix games. MOL performs well in competitive games played against different opponents and converges to stable points that score above the Nash equilibrium in repeated game environments. The results may provide a reference for the definition of equilibrium in multiagent reinforcement learning systems, and contribute to the design of learning objectives in MARL to avoid local disadvantageous equilibrium and improve general efficiency.