Cooperation in collective risk dilemmas with endogenous heterogeneity: Nash equilibrium and evolutionary dynamics

This paper presents a novel method for analyzing the economic and collaborative interactions among nations in the context of climate change. Specifically, a two-stage game-theoretic model is proposed, where players’ initial resources (heterogeneous endowments) are determined by a public goods game (first-stage) and a collective risk dilemma is subsequently played (second-stage). We establish the Nash equilibria for the proposed game model and provide numerical analysis results accordingly. We then explore the dynamics of the game in an evolutionary process, dividing the population into groups of fixed size. Our findings indicate that the scenario with high collective risk and low required donation is most conducive to cooperation, while smaller groups and populations are more likely to exhibit cooperative behavior. Moreover, both numerical analysis and simulation results demonstrate that a higher first-stage profit rate enhances cooperation. Overall, our study sheds light on the factors that facilitate cooperation among multiple heterogeneously endowed participants facing collective risk. We hope that our proposed model and results can contribute to the development of solutions for addressing the challenges posed by global issues such as climate change.