# Coevolutionary dynamics of cooperation, risk, and cost in collective risk games

## TL;DR

The paper studies how cooperation, risk, and cost interact in collective decision-making scenarios, showing that initial conditions determine whether cooperation or failure emerges.

## Contribution

A novel evolutionary game model is introduced that captures the coevolution of cooperation, risk, and cost in collective-risk dilemmas.

## Key findings

- Stable cooperation can emerge in low-risk environments with minimal cooperation costs.
- The system supports multistability, leading to either cooperation or a tragedy of the commons depending on initial conditions.
- Full defection with maximum risk and cost remains a stable evolutionary attractor.

## Abstract

Addressing both natural and societal challenges requires collective cooperation. Studies on collective-risk social dilemmas have shown that individual decisions are influenced by the perceived risk of collective failure. However, existing feedback-evolving game models often focus on a single feedback mechanism, such as the coupling between cooperation and risk or between cooperation and cost. In many real-world scenarios, however, the level of cooperation, the cost of cooperating, and the collective risk are dynamically interlinked. Here, we present an evolutionary game model that considers the interplay of these three variables. Our analysis shows that the worst-case scenario, characterized by full defection, maximum risk, and the highest cost of cooperation, remains a stable evolutionary attractor. Nevertheless, cooperation can emerge and persist because the system also supports stable equilibria with non-zero cooperation. The system exhibits multistability, meaning that different initial conditions lead to either sustained cooperation or a tragedy of the commons. These findings highlight that initial levels of cooperation, cost, and risk collectively determine whether a population can avert a tragic outcome.

Collective cooperation is indispensable for addressing natural and social challenges. Prior research on collective-risk social dilemmas has shown that individual contributions are shaped by the risk of collective failure, yet it insufficiently captures a key complexity: the intricate interdependencies among cooperation cost, collective failure risk, and cooperation level. Here, we develop an evolutionary game model with a multiple feedback mechanism to clarify cooperative behavior emergence in complex gaming contexts. We find that this tightly coupled system yields diverse dynamic outcomes. Notably, individuals can sustain stable cooperation in low-risk environments with only minimal cooperation costs. However, the “tragedy of the commons", a state of universal free-riding with maximum risk and cooperation costs is always attainable in our model. Critical factors for escaping this dilemma include the initial cooperation rate, cooperation cost, and risk value.