Emergence of cooperation in a population with bimodal response behaviors

TL;DR

This study investigates how bimodal response behaviors, specifically Fermi and Tit-for-tat strategies, influence the evolution of cooperation in populations, revealing that behavioral diversity can significantly promote cooperative outcomes.

Contribution

The paper introduces a model combining Fermi and Tit-for-tat updating rules to show how behavioral multimodality enhances cooperation in structured and probabilistic mixing scenarios.

Findings

Moderate mixture of response modes boosts cooperation.

Probabilistic mixing leads to widespread full cooperation.

Robustness of results across different population topologies.

Abstract

We human beings show remarkable adaptability in response to complex surroundings, we adopt different behavioral modes at different occasions, such response multimodality is critical to our survival. Yet, how this behavioral multimodality affects the evolution of cooperation remains largely unknown. Here we build a toy model to address this issue by considering a population with bimodal response behaviors, or specifically, with the Fermi and Tit-for-tat updating rules. While the former rule tends to imitate the strategies of those neighbors who are doing well, the latter repeats what their neighbors did to them. In a structural mixing implementation, where the updating rule is fixed for each individual, we find that a moderate mode mixture unexpectedly boosts the overall cooperation level of the population. The boost is even more pronounced in the probabilistic mixing, where each individual randomly chooses one of the two modes at each step, and full cooperation is seen in a wide range. These findings are robust to the underlying topology of the population. Our mean-field treatment reveals that the cooperation prevalence within the players with the Fermi rule linearly increases with the fraction of TFT players and explains the non-monotonic dependence in the structural mixing. Our study shows that the diversity in response behaviors may help to explain the emergence of cooperation in realistic contexts.