Evolutionary games with environmental feedbacks under an external incentive mechanism

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 coevolu-tion. 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'.