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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. • New game-theoretical method models interactions among nations facing global risks. • A two-stage game model considers endogenously generated heterogeneous endowments. • Nash equilibria and evolutionary dynamics of the game are studied. • Factors favoring cooperation are given with theoretical/numerical/simulation results. [ABSTRACT FROM AUTHOR]

An interest coalition of sharing benefits and risks, such as cross shareholding between companies, allows them to transfer risks in a competitive business world. In a public goods game, cooperators are at the risk of being exploited by defectors. This paper studies whether such risk-transfer mechanism can induce cooperative behaviors in social dilemmas. We model a public goods game with coalition mechanism in a structured population. The players are categorized by whether they cooperate as well as whether they are willing to form coalitions. Those who are willing (unwilling) to form coalitions with others are called coalitional (traditional) individuals. By exploring the phase transitions of systems, the spatial dynamics of some phases and the evolution of characteristic spatial distributions of strategies, we study the effect of this mechanism on cooperation. The results show that the positive (negative) impact of such interest coalitions on the competitiveness of cooperators (defectors) can be improved as the closeness of interest relationship within coalitions increases. However, this does not mean that a closer coalition can absolutely increase the overall level of cooperation in a more complex four-strategy system. This is related to the transformation from CCs (coalitional cooperators) to TDs (traditional defectors) due to CCs' breaking of the encirclement formed by CDs (coalitional defectors) at a low synergy coefficient, as well as the invasion of TCs (traditional cooperators) to CCs at the boundary separating CCs, TCs and TDs at a high synergy coefficient. [ABSTRACT FROM AUTHOR]

• A model to study why donation behaviors are prevalent in donation games. • Spatial dynamics are studied to explore the underlying mechanism of some phases. • Extreme altruists cannot survive with extreme egoists unless they become shunners. • Hypocrites and realists will hinder the spread of donation behaviors. Unlike in the standard public goods game (PGG), real-life donors (e.g. to charities) rarely receive any direct benefits from their donation behaviors to a disaster area, but donations are always prevalent. This paper studies why donation behaviors are common and the factors that can influence their propagation. The interactions among individuals are divided into two phases, including all individuals independently making decisions about whether to donate (namely donation game) and playing prisoner's dilemma with their neighbors in a structured population. We first explore the evolution of donation behaviors in the aforementioned spatial games with four competing strategies. As expected, "extreme altruists" can hardly survive in the population with "extreme egoists" unless they become "shunners", who decide whether to cooperate in the prisoner's dilemma on the basis of the reputation of their opponents. Given the complexity of the real world, we further study the evolution of a more complex six-strategy population with additional two peculiar strategies, "hypocrites" and "realists". We have observed more complicated phase diagrams, and multiple discontinuous phase transitions as well as a variety of spontaneously formed three-strategy cyclic states. Through the analysis of the phases and spatial dynamics, we find that these two introduced strategies will have an adverse impact on the popularization of donation behaviors in their own ways under different circumstances. [ABSTRACT FROM AUTHOR]

Compared with the mandatory personal carbon trading, mechanisms that encourage individuals to voluntarily participate in carbon emission reduction are more easily accepted, such as the CGSP (Carbon Generalized System of Preferences) project in Guangdong Province, China. Carbon emission reduction, as a joint effort of multiple generations, involves interest conflicts between individuals and groups in one single generation, as well as multigenerational conflicts. By establishing the interaction between local environmental quality and individual returns, we build a public goods game with environmental feedback to simulate ecological and social coevolution. In this game with the CGSP mechanism, cooperators who reduce carbon emissions receive carbon credits, with which they can exchange for welfare funds to invest in environmental protection (denoted as AC) or for goods to improve their personal payoffs (BC). Individuals who do not contribute anything to improve the environment are called defectors (D). To study the impact of CGSP as an external incentive mechanism on cooperation, we explore the stationary states of three systems. In addition, we study the mechanisms behind some phases and phase transitions by monitoring the spatial distribution of strategies and the environmental quality of each region. The results show that a higher subsidy is not always better, whether cooperators exchange carbon credits for goods or welfare funds. Furthermore, ACs can effectively improve the spatial competitiveness of BC clusters, but BCs as 'second-order free-riders' can inhibit the spread of ACs. Indirect territorial competition between two types of cooperators can solve such a 'second-order social dilemma'. [ABSTRACT FROM AUTHOR]

Although cooperative behavior is ubiquitous in biological and social systems, the causes and mechanisms of cooperation are a basic problem in evolutionary theory. The snowdrift game is considered as an effective evolutionary game model to describe cooperative behavior in a competitive situation. Thus, this paper studies the evolutionary dynamics of cooperative behavior in multi-player snowdrift games. This work establishes a stochastic two-strategy multi-player snowdrift game based on the Wright-Fisher (W-F) update process. Next, a specific analytical expression for fixation probabilities of cooperation and defection is considered, and the conditions under which cooperative strategies take root in a population and become an evolutionarily stable strategy are given. Finally, the relationships between the fixation probability of cooperation and each parameter involved in the game are obtained via simulation analysis. A simulation analysis reveals that the fixation probability of cooperation decreases with selection intensity, the number of players playing in multi-player snowdrift games, and population size but increases with the benefit-cost ratio. The present work promotes an understanding of the evolutionary dynamics of cooperative behavior and the theory of multi-player snowdrift games with the W-F update process. • A two-strategy multi-player snowdrift game with a W-F process is established. • The concrete analytic expression of the fixation probability is solved. • The conditions under which a strategy takes root and becomes ESS are given. • The relationships between fixation probability and each parameter are obtained. [ABSTRACT FROM AUTHOR]