Satisfied-defect, unsatisfied-cooperate: An evolutionary dynamics of cooperation led by aspiration

TL;DR

This paper introduces a new aspiration-led strategy update mechanism in evolutionary game theory, demonstrating its richer behavioral dynamics in Prisoner's Dilemma games through analytical and numerical analysis.

Contribution

It proposes a novel aspiration-led update rule called 'Satisfied-Defect, Unsatisfied-Cooperate' and explores its effects on cooperation evolution, filling a gap in existing aspiration-based models.

Findings

The new update rule produces more diverse behaviors than traditional aspiration updates.

Analytical and numerical results show complex dynamics in finite and infinite populations.

The mechanism better aligns with behavioral experiment observations.

Abstract

Evolutionary game theory has been widely used to study the evolution of cooperation in social dilemmas where imitation-led strategy updates are typically assumed. However, results of recent behavioral experiments are not compatible with the predictions based on the imitation dynamics, casting doubts on the assumption of the imitation-led updates and calling for alternative mechanisms of strategy updates. An aspiration-led update is often considered as an alternative to the imitation-led one. While details of update rules can have significant impacts on the evolutionary outcomes and many variations in imitation-led updates are thus studied, however, few variations exist in aspiration-led updates. We introduce an aspiration-led update mechanism ("Satisfied-Defect, Unsatisfied-Cooperate") that is psychologically intuitive and can yield a behavior richer than the conventional aspiration-led update does in Prisoner's Dilemma games. Using analytical and numerical methods, we study and link the stochastic dynamics of it in well-mixed finite populations and the deterministic dynamics of infinite populations.