Numerical analysis of a reinforcement learning model with the dynamic aspiration level in the iterated Prisoner's Dilemma

TL;DR

This paper numerically analyzes a reinforcement learning model with dynamic aspiration levels in the iterated Prisoner's Dilemma, demonstrating conditions for cooperation and evolutionary invasion of learning strategies.

Contribution

It introduces a simplified, flexible reinforcement learning model with dynamic thresholds, showing its effectiveness in promoting cooperation and evolutionary invasion.

Findings

Mutual cooperation occurs when threshold dynamics are not too fast.

Learning players perform well against reactive strategies.

Learning strategies can invade populations of simpler strategies.

Abstract

Humans and other animals can adapt their social behavior in response to environmental cues including the feedback obtained through experience. Nevertheless, the effects of the experience-based learning of players in evolution and maintenance of cooperation in social dilemma games remain relatively unclear. Some previous literature showed that mutual cooperation of learning players is difficult or requires a sophisticated learning model. In the context of the iterated Prisoner's Dilemma, we numerically examine the performance of a reinforcement learning model. Our model modifies those of Karandikar et al. (1998), Posch et al. (1999), and Macy and Flache (2002) in which players satisfice if the obtained payoff is larger than a dynamic threshold. We show that players obeying the modified learning mutually cooperate with high probability if the dynamics of threshold is not too fast and the association between the reinforcement signal and the action in the next round is sufficiently strong. The learning players also perform efficiently against the reactive strategy. In evolutionary dynamics, they can invade a population of players adopting simpler but competitive strategies. Our version of the reinforcement learning model does not complicate the previous model and is sufficiently simple yet flexible. It may serve to explore the relationships between learning and evolution in social dilemma situations.