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

TL;DR

This paper introduces a coevolutionary game model linking cooperation, risk, and cost, revealing conditions for sustained cooperation and multistability in collective risk dilemmas.

Contribution

It develops a novel evolutionary game model that captures the dynamic interplay of cooperation, risk, and cost, extending previous models with a more comprehensive feedback mechanism.

Findings

Full defection and high risk are stable attractors.

Cooperation can emerge and persist under certain conditions.

Initial states influence long-term outcomes and stability.

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.