Learning in Multi-Memory Games Triggers Complex Dynamics Diverging from Nash Equilibrium

Author name not available (Why is that?)

Publication date: 2 February 2023

Abstract: Repeated games consider a situation where multiple agents are motivated by their independent rewards throughout learning. In general, the dynamics of their learning become complex. Especially when their rewards compete with each other like zero-sum games, the dynamics often do not converge to their optimum, i.e., the Nash equilibrium. To tackle such complexity, many studies have understood various learning algorithms as dynamical systems and discovered qualitative insights among the algorithms. However, such studies have yet to handle multi-memory games (where agents can memorize actions they played in the past and choose their actions based on their memories), even though memorization plays a pivotal role in artificial intelligence and interpersonal relationship. This study extends two major learning algorithms in games, i.e., replicator dynamics and gradient ascent, into multi-memory games. Then, we prove their dynamics are identical. Furthermore, theoretically and experimentally, we clarify that the learning dynamics diverge from the Nash equilibrium in multi-memory zero-sum games and reach heteroclinic cycles (sojourn longer around the boundary of the strategy space), providing a fundamental advance in learning in games.

Has companion code repository: https://github.com/cyberagentailab/with-memory_games

This page was built for publication: Learning in Multi-Memory Games Triggers Complex Dynamics Diverging from Nash Equilibrium

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6425213)