# Oscillatory evolution of collective behavior in evolutionary games played with reinforcement learning

## TL;DR

This paper explores how reinforcement learning influences collective behavior in evolutionary games, revealing oscillatory cooperation patterns and providing insights into natural and societal emergence of cooperation.

## Contribution

It introduces RL into evolutionary game dynamics, demonstrating oscillatory cooperation and analyzing the impact of payoff structures on these behaviors.

## Key findings

- Reinforcement learning induces oscillatory cooperation in certain games.
- Cooperation levels in AI agents are comparable to traditional evolutionary games.
- Oscillatory behaviors are observed in multiple game types, including snowdrift and rock-paper-scissors.

## Abstract

Large-scale cooperation underpins the evolution of ecosystems and the human society, and the collective behaviors by self-organization of multi-agent systems are the key for understanding. As artificial intelligence (AI) prevails in almost all branches of science, it would be of great interest to see what new insights of collective behavior could be obtained from a multi-agent AI system. Here, we introduce a typical reinforcement learning (RL) algorithm -- Q learning into evolutionary game dynamics, where agents pursue optimal action on the basis of the introspectiveness rather than the birth-death or imitation processes in the traditional evolutionary game (EG). We investigate the cooperation prevalence numerically for a general $2\times 2$ game setting. We find that the cooperation prevalence in the multi-agent AI is amazing of an equal level as in the traditional EG in most cases. However, in the snowdrift games with RL we also reveal that explosive cooperation appears in the form of periodic oscillation, and we study the impact of the payoff structure on its emergence. Finally, we show that the periodic oscillation can also be observed in some other EGs with the RL algorithm, such as the rock-paper-scissors game. Our results offer a reference point to understand emergence of cooperation and oscillatory behaviors in nature and society from AI's perspective.