Evolution of conditional cooperation in collective-risk social dilemma with repeated group interactions

TL;DR

This paper develops a theoretical evolutionary game model to study how conditional cooperation strategies influence the emergence and stability of cooperation in repeated collective-risk social dilemmas, highlighting the roles of risk levels and thresholds.

Contribution

It introduces a novel model incorporating conditional strategies based on risk tolerance and collective goals, revealing their impact on cooperation evolution in repeated interactions.

Findings

Conditional cooperation promotes cooperation, especially at low risk levels.

Higher risk thresholds encourage the emergence of cooperative behavior.

Timely shifts from defection to cooperation help sustain high cooperation levels.

Abstract

The evolution and long-term sustenance of cooperation has consistently piqued scholarly interest across the disciplines of evolutionary biology and social sciences. Previous theoretical and experimental studies on collective risk social dilemma games have revealed that the risk of collective failure will affect the evolution of cooperation. In the real world individuals usually adjust their decisions based on environmental factors such as risk intensity and cooperation level. However, it is still not well understood how such conditional behaviors affect the evolution of cooperation in repeated group interactions scenario from a theoretical perspective. Here, we construct an evolutionary game model with repeated interactions, in which defectors decide whether to cooperate in subsequent rounds of the game based on whether the risk exceeds their tolerance threshold and whether the number of cooperators exceeds the collective goal in the early rounds of the game. We find that the introduction of conditional cooperation strategy can effectively promote the emergence of cooperation, especially when the risk is low. In addition, the risk threshold significantly affects the evolutionary outcomes, with a high risk promoting the emergence of cooperation. Importantly, when the risk of failure to reach collective goals exceeds a certain threshold, the timely transition from a defective strategy to a cooperative strategy by conditional cooperators is beneficial for maintaining high-level cooperation.